• Title/Summary/Keyword: fractional error

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ANALYSIS OF SOME PROJECTION METHODS FOR THE INCOMPRESSIBLE FLUIDS WITH MICROSTRUCTURE

  • Jiang, Yao-Lin;Yang, Yun-Bo
    • Journal of the Korean Mathematical Society
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    • v.55 no.2
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    • pp.471-506
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    • 2018
  • In this article, some projection methods (or fractional-step methods) are proposed and analyzed for the micropolar Navier-Stokes equations (MNSE). These methods allow us to decouple the MNSE system into two sub-problems at each timestep, one is the linear and angular velocities system, the other is the pressure system. Both first-order and second-order projection methods are considered. For the classical first-order projection scheme, the stability and error estimates for the linear and angular velocities and the pressure are established rigorously. In addition, a modified first-order projection scheme which leads to some improved error estimates is also proposed and analyzed. We also present the second-order projection method which is unconditionally stable. Ample numerical experiments are performed to confirm the theoretical predictions and demonstrate the efficiency of the methods.

Estimation of Fractional Urban Tree Canopy Cover through Machine Learning Using Optical Satellite Images (기계학습을 이용한 광학 위성 영상 기반의 도시 내 수목 피복률 추정)

  • Sejeong Bae ;Bokyung Son ;Taejun Sung ;Yeonsu Lee ;Jungho Im ;Yoojin Kang
    • Korean Journal of Remote Sensing
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    • v.39 no.5_3
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    • pp.1009-1029
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    • 2023
  • Urban trees play a vital role in urban ecosystems,significantly reducing impervious surfaces and impacting carbon cycling within the city. Although previous research has demonstrated the efficacy of employing artificial intelligence in conjunction with airborne light detection and ranging (LiDAR) data to generate urban tree information, the availability and cost constraints associated with LiDAR data pose limitations. Consequently, this study employed freely accessible, high-resolution multispectral satellite imagery (i.e., Sentinel-2 data) to estimate fractional tree canopy cover (FTC) within the urban confines of Suwon, South Korea, employing machine learning techniques. This study leveraged a median composite image derived from a time series of Sentinel-2 images. In order to account for the diverse land cover found in urban areas, the model incorporated three types of input variables: average (mean) and standard deviation (std) values within a 30-meter grid from 10 m resolution of optical indices from Sentinel-2, and fractional coverage for distinct land cover classes within 30 m grids from the existing level 3 land cover map. Four schemes with different combinations of input variables were compared. Notably, when all three factors (i.e., mean, std, and fractional cover) were used to consider the variation of landcover in urban areas(Scheme 4, S4), the machine learning model exhibited improved performance compared to using only the mean of optical indices (Scheme 1). Of the various models proposed, the random forest (RF) model with S4 demonstrated the most remarkable performance, achieving R2 of 0.8196, and mean absolute error (MAE) of 0.0749, and a root mean squared error (RMSE) of 0.1022. The std variable exhibited the highest impact on model outputs within the heterogeneous land covers based on the variable importance analysis. This trained RF model with S4 was then applied to the entire Suwon region, consistently delivering robust results with an R2 of 0.8702, MAE of 0.0873, and RMSE of 0.1335. The FTC estimation method developed in this study is expected to offer advantages for application in various regions, providing fundamental data for a better understanding of carbon dynamics in urban ecosystems in the future.

A Study on the Long-Run Equilibrium Between KOSPI 200 Index Spot Market and Futures Market (분수공적분을 이용한 KOSPI200지수의 현.선물 장기균형관계검정)

  • Kim, Tae-Hyuk;Lim, Soon-Young;Park, Kap-Je
    • The Korean Journal of Financial Management
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    • v.25 no.3
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    • pp.111-130
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    • 2008
  • This paper compares long term equilibrium relation of KOSPI 200 which is underling stock and its futures by using general method fractional cointegration instead of existing integer cointegration. Existence of integer cointegration between two price time series gives much wider information about long term equilibrium relation. These details grasp long term equilibrium relation of two price time series as well as reverting velocity to equilibrium by observing difference coefficient of error term when it renounces from equilibrium relation. The result of this study reveals existence of long term equilibrium relation between KOSPI200 and futures which follow fractional cointegration. Difference coefficient, d, of 'two price time series error term' satisfies 0 < d < 1/2 beside bandwidth parameter, m(173). It means two price time series follow stationary long memory process. This also means impulse effects to balance price of two price time series decrease gently within hyperbolic rate decay. It indicates reverting speed of error term is very low when it bolts from equilibrium. It implies to market maker, who is willing to make excess return with arbitrage trading and hedging risk using underling stock, how invest strategy should be changed. It also insinuates that information transition between KOSPI 200 Index market and futures market does not working efficiently.

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A Numerically Controlled Oscillator with a Fine Phase Tuner and a Rounding Processor

  • Lim, In-Gi;Kim, Whan-Woo
    • ETRI Journal
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    • v.26 no.6
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    • pp.657-660
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    • 2004
  • We propose a fine phase tuner and a rounding processor for a numerically controlled oscillator (NCO), yielding a reduced phase error in generating a digital sine waveform. By using the fine phase tuner presented in this paper, when the ratio of the desired sine wave frequency to the clock frequency is expressed as a fraction, an accurate adjustment in representing the fractional value can be achieved with simple hardware. In addition, the proposed rounding processor reduces the effects of phase truncation on the output spectrum. Logic simulation results of the NCO using these techniques show that the noise spectrum and mean square error (MSE) for eight output bits of a 3.125 MHz sine waveform are reduced by 8.68 dB and 5.5 dB, respectively, compared to those of the truncation method, and 2.38 dB and 0.83 dB, respectively, compared to those of Paul's scheme.

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A robust frequency offset estimation scheme for an OFDM system (OFDM 수신기를 위한 강인한 주파수 옵셋 보정 기법)

  • Wui, Jung-Hwa;Hwang, Hu-Mor;Song, Jin-Ho
    • Proceedings of the KIEE Conference
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    • 2000.07d
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    • pp.3100-3102
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    • 2000
  • In this paper, we propose to a robust frequency offset estimation method of OFDM signals. A carrier frequency offset may be decomposed into an integer multiple of the subcarrier spacing and a residual frequency offset. Fractional part of frequency offset is obtained by using the maximum likelihood estimation(MLE) method. And we use the correlation of the samples at the output of the discrete Fourier transform(DFT) to estimate integer part of frequency offset. The result shows that the estimation frequency offset is almost linear to frequency offset. We propose to an improved estimation error variance of the carrier frequency offset estimation. The proposed estimator has better performance than the conventional ones in terms of error variance and tracking range.

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Nonlinear optimization algorithm using monotonically increasing quantization resolution

  • Jinwuk Seok;Jeong-Si Kim
    • ETRI Journal
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    • v.45 no.1
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    • pp.119-130
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    • 2023
  • We propose a quantized gradient search algorithm that can achieve global optimization by monotonically reducing the quantization step with respect to time when quantization is composed of integer or fixed-point fractional values applied to an optimization algorithm. According to the white noise hypothesis states, a quantization step is sufficiently small and the quantization is well defined, the round-off error caused by quantization can be regarded as a random variable with identically independent distribution. Thus, we rewrite the searching equation based on a gradient descent as a stochastic differential equation and obtain the monotonically decreasing rate of the quantization step, enabling the global optimization by stochastic analysis for deriving an objective function. Consequently, when the search equation is quantized by a monotonically decreasing quantization step, which suitably reduces the round-off error, we can derive the searching algorithm evolving from an optimization algorithm. Numerical simulations indicate that due to the property of quantization-based global optimization, the proposed algorithm shows better optimization performance on a search space to each iteration than the conventional algorithm with a higher success rate and fewer iterations.

A Joint Frequency Offset Measurement Using Inversely Repeated Training Symbol and Cyclic Prefix (훈련심볼의 위상 반전과 전치순환을 이용한 주파수 오프셋의 계산방법)

  • Kim, Jun-Woo;Park, Youn-Ok;Kim, Whan-Woo
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.36 no.7A
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    • pp.627-634
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    • 2011
  • In this paper, a new frequency offset estimation method in OFDM system is suggested. To measure fractional part of frequency offset, the repetition feature of cyclic prefix and that of training sequence is adopted. Both method shows relatively large frequency offset estimation error under low SNR circumstances, but this error can be greatly reduced by joint measurement of cyclic prefix and inversely repeated training symbol such as primary advanced preamble (PA-preamble) of IEEE 802.16m IMT-Advanced WiMax system. In this paper, the performance of suggested frequency offset estimation method is verified in IEEE 802.16m IMT Advanced WiMax system, using its PA-preamble and cyclic prefixes of A-preambles.

TIME SERIES PREDICTION USING INCREMENTAL REGRESSION

  • Kim, Sung-Hyun;Lee, Yong-Mi;Jin, Long;Chai, Duck-Jin;Ryu, Keun-Ho
    • Proceedings of the KSRS Conference
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    • v.2
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    • pp.635-638
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    • 2006
  • Regression of conventional prediction techniques in data mining uses the model which is generated from the training step. This model is applied to new input data without any change. If this model is applied directly to time series, the rate of prediction accuracy will be decreased. This paper proposes an incremental regression for time series prediction like typhoon track prediction. This technique considers the characteristic of time series which may be changed over time. It is composed of two steps. The first step executes a fractional process for applying input data to the regression model. The second step updates the model by using its information as new data. Additionally, the model is maintained by only recent data in a queue. This approach has the following two advantages. It maintains the minimum information of the model by using a matrix, so space complexity is reduced. Moreover, it prevents the increment of error rate by updating the model over time. Accuracy rate of the proposed method is measured by RME(Relative Mean Error) and RMSE(Root Mean Square Error). The results of typhoon track prediction experiment are performed by the proposed technique IMLR(Incremental Multiple Linear Regression) is more efficient than those of MLR(Multiple Linear Regression) and SVR(Support Vector Regression).

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Orthogonal variable spreading factor encoded unmanned aerial vehicle-assisted nonorthogonal multiple access system with hybrid physical layer security

  • Omor Faruk;Joarder Jafor Sadiqu;Kanapathippillai Cumanan;Shaikh Enayet Ullah
    • ETRI Journal
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    • v.45 no.2
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    • pp.213-225
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    • 2023
  • Physical layer security (PLS) can improve the security of both terrestrial and nonterrestrial wireless communication networks. This study proposes a simplified framework for nonterrestrial cyclic prefixed orthogonal variable spreading factor (OVSF)-encoded multiple-input and multiple-output nonorthogonal multiple access (NOMA) systems to ensure complete network security. Various useful methods are implemented, where both improved sine map and multiple parameter-weighted-type fractional Fourier transform encryption schemes are combined to investigate the effects of hybrid PLS. In addition, OVSF coding with power domain NOMA for multi-user interference reduction and peak-toaverage power ratio (PAPR) reduction is introduced. The performance of $\frac{1}{2}$-rated convolutional, turbo, and repeat and accumulate channel coding with regularized zero-forcing signal detection for forward error correction and improved bit error rate (BER) are also investigated. Simulation results ratify the pertinence of the proposed system in terms of PLS and BER performance improvement with reasonable PAPR.

ON MEASURING THE WELDING TEMPERATURE OF CONNECTOR

  • Deng Jyh-jeng
    • Proceedings of the Korean Society for Quality Management Conference
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    • 1998.11a
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    • pp.361-377
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    • 1998
  • The measurement of welding temperature of connector is usually performed with an infra red temperature gauge. However, the factors, which influence the temperature measurement, are rarely known. This research used the welding temperature measurement of the connector as an example, applying the experimental design, in two-phase experiments, to search the affecting factors. In phase-I experiment, we used a resolution III, seven-factor fractional factorial design with two levels for each factor. The result showed that none of the factor was significant in affecting the welding temperature when the type I error ${\alpha}$ was 0.05. Next, we did the phase-II factorial experiment with three factors and each factor had three levels. The experiment showed the experimental time was significant in affecting the temperature measurement when the type I error ${\alpha}$ was 0.05. Further Duncan's multiple range tests on the second experimental data showed that the later the experimental time, the weaker the light intensity could have on the temperature measurement and the average of the highest temperatures was lower. Moreover, the later the experimental time, the smaller was the variance of the temperature measurement and the difference between the averages of the highest and the lowest temperatures was also lower.

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