• Title/Summary/Keyword: error distribution

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Site-Specific Error-Cross Correlation-Informed Quadruple Collocation Approach for Improved Global Precipitation Estimates

  • Alcantara, Angelika;Ahn Kuk-Hyun
    • Proceedings of the Korea Water Resources Association Conference
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    • 2023.05a
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    • pp.180-180
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    • 2023
  • To improve global risk management, understanding the characteristics and distribution of precipitation is crucial. However, obtaining spatially and temporally resolved climatic data remains challenging due to sparse gauge observations and limited data availability, despite the use of satellite and reanalysis products. To address this challenge, merging available precipitation products has been introduced to generate spatially and temporally reliable data by taking advantage of the strength of the individual products. However, most of the existing studies utilize all the available products without considering the varying performances of each dataset in different regions. Comprehensively considering the relative contributions of each parent dataset is necessary since their contributions may vary significantly and utilizing all the available datasets for data merging may lead to significant data redundancy issues. Hence, for this study, we introduce a site-specific precipitation merging method that utilizes the Quadruple Collocation (QC) approach, which acknowledges the existence of error-cross correlation between the parent datasets, to create a high-resolution global daily precipitation data from 2001-2020. The performance of multiple gridded precipitation products are first evaluated per region to determine the best combination of quadruplets to be utilized in estimating the error variances through the QC approach and computation of merging weights. The merged precipitation is then computed by adding the precipitation from each dataset in the quadruplet multiplied by each respective merging weight. Our results show that our approach holds promise for generating reliable global precipitation data for data-scarce regions lacking spatially and temporally resolved precipitation data.

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Adaptive Extraction Method for Phase Foreground Region in Laser Interferometry of Gear

  • Xian Wang;Yichao Zhao;Chaoyang Ju;Chaoyong Zhang
    • Current Optics and Photonics
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    • v.7 no.4
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    • pp.387-397
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    • 2023
  • Tooth surface shape error is an important parameter in gear accuracy evaluation. When tooth surface shape error is measured by laser interferometry, the gear interferogram is highly distorted and the gray level distribution is not uniform. Therefore, it is important for gear interferometry to extract the foreground region from the gear interference fringe image directly and accurately. This paper presents an approach for foreground extraction in gear interference images by leveraging the sinusoidal variation characteristics shown by the interference fringes. A gray level mask with an adaptive threshold is established to capture the relevant features, while a local variance evaluation function is employed to analyze the fluctuation state of the interference image and derive a repair mask. By combining these masks, the foreground region is directly extracted. Comparative evaluations using qualitative and quantitative assessment methods are performed to compare the proposed algorithm with both reference results and traditional approaches. The experimental findings reveal a remarkable degree of matching between the algorithm and the reference results. As a result, this method shows great potential for widespread application in the foreground extraction of gear interference images.

New mathematical approach to determine solar radiation for the southwestern coastline of Pakistan

  • Atteeq Razzak;Zaheer Uddin;M. Jawed Iqbal
    • Advances in Energy Research
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    • v.8 no.2
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    • pp.111-123
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    • 2022
  • Solar Energy is the energy of solar radiation carried by them in the form of heat and light. It can be converted into electricity. Solar potential depends on the site's atmosphere; the solar energy distribution depends on many factors, e.g., turbidity, cloud types, pollution levels, solar altitude, etc. We estimated solar radiation with the help of the Ashrae clear-sky model for three locations in Pakistan, namely Pasni, Gwadar, and Jiwani. As these locations are close to each other as compared to the distance between the sun and earth, therefore a slight change of latitude and longitude does not make any difference in the calculation of direct beam solar radiation (BSR), diffuse solar radiation (DSR), and global solar radiation (GSR). A modified formula for declination angle is also developed and presented. We also created two different models for Ashrae constants. The values of these constants are compared with the standard Ashrae Model. A good agreement is observed when we used these constants to calculate BSR, DSR, GSR, the Root mean square error (RMSE), Mean Absolute error (MABE), Mean Absolute percent error (MAPE), and chisquare (χ2) values are in acceptance range, indicating the validity of the models.

Effects of Walking Training according to Rhythmic Auditory Stimulation Speed Control Balance of Stroke Patients

  • Jin Park;Taeho Kim
    • The Journal of Korean Physical Therapy
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    • v.35 no.6
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    • pp.213-219
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    • 2023
  • Purpose: In this study, based on the error augmentation, we performed walking training with increased rhythmic auditory stimulation speed on the affected side (IRAS) and walking training with decreased rhythmic auditory stimulation speed on the unaffected side (DRAS). The purpose of this study was to verify whether motor learning was effective in improving balance ability. Methods: Twenty-eight subjects with chronic stroke were recruited from a rehabilitation center. The subjects were divided into three groups: an IRAS group (10 subjects), a DRAS group (9 subjects), and control group (9 subjects). They received 30minutes of neuro-developmental therapy and walking training for 30minutes, five times a week for three weeks. Static and functional balance ability were measured before and after the training period. Static balance was measured by balancia software. Functional balance was measured by the timed up and go test (TUG) and the berg balance scale (BBS). Results: After the training periods, the IRAS group showed a significant improvement in TUG, BBS, area 95% COP, and weight distribution on the affected side when compared to both the DRAS group and control group (p<0.05). Conclusion: Based on the results of this study, it is possible to consider error augmentation methods of motor learning if rhythmic auditory stimulation is applied to stroke patients in clinical practice. If the affected side is shorter than the unaffected side, the affected side should be adjusted to the increased rhythmic auditory stimulation speed, which is considered to be an effective intervention to improve balance ability.

Objective Bayesian Estimation of Two-Parameter Pareto Distribution (2-모수 파레토분포의 객관적 베이지안 추정)

  • Son, Young Sook
    • The Korean Journal of Applied Statistics
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    • v.26 no.5
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    • pp.713-723
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    • 2013
  • An objective Bayesian estimation procedure of the two-parameter Pareto distribution is presented under the reference prior and the noninformative prior. Bayesian estimators are obtained by Gibbs sampling. The steps to generate parameters in the Gibbs sampler are from the shape parameter of the gamma distribution and then the scale parameter by the adaptive rejection sampling algorism. A numerical study shows that the proposed objective Bayesian estimation outperforms other estimations in simulated bias and mean squared error.

On the Method of Rankine Source Distribution for Free Surface Flow Problem: Radiation Condition and Influence of Finite Distribution (자유표면문제해석(자유표면문제해석)을 위한 Rankine용출점(湧出點) 분포법(分布法) -방사조건(放射條件)과 유한분포(有限分布)의 영향-)

  • Chang-Sup,Lee;Seung-Il,Yang;Chang-Gu,Kang
    • Bulletin of the Society of Naval Architects of Korea
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    • v.19 no.2
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    • pp.13-18
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    • 1982
  • The method of Rankine source distribution is emerging as a powerful yet simple alternative for the solution of complicated free surface problems. But it has been uncertain whether the radiation condition could be satisfied exactly by distributing the simple sources on the free surface only. In this paper, it is proved rigorously that the Rankine sources, whose intensities are varying sinusoidally along the axis satisfying the free surface boundary condition, generate the radiation waves both in the infinite and finite-depth flows. A formula is derived to give the upper and lower bounds of the errors in the induced velocity computation that will be introduced by truncating the extent of source distribution on the free surface. Since the truncation is inevitable in the numerical analysis, this formula may be used as a criterion to limit the position of the field points, where velocity computation is made, away from the truncation boundary. A typical analysis shows that the maximum error will be 3.4 percent of the exact induced velocity when the field point is on the free surface two wave lengths away from the truncation boundary.

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The Comparative Study based on Gompertz Software Reliability Model of Shape Parameter (곰페르츠형 형상모수에 근거한 소프트웨어 신뢰성모형에 대한 비교연구)

  • Shin, Hyun Cheul;Kim, Hee Cheul
    • Journal of Korea Society of Digital Industry and Information Management
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    • v.10 no.2
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    • pp.29-36
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    • 2014
  • Finite failure NHPP software reliability models presented in the literature exhibit either constant, monotonic increasing or monotonic decreasing failure occurrence rates per fault. In this paper, proposes the Gompertz distribution reliability model, which made out efficiency application for software reliability. Algorithm to estimate the parameters used to maximum likelihood estimator and bisection method, model selection based on mean square error (MSE) and coefficient of determination$(R^2)$, for the sake of efficient model, was employed. Analysis of failure using real data set for the sake of proposing fixed shape parameter of the Gompertz distribution was employed. This analysis of failure data compared with the Gompertz distribution model of shape parameter. In order to insurance for the reliability of data, Laplace trend test was employed. In this study, the proposed Gompertz model is more efficient in terms of reliability in this area. Thus, Gompertz model can also be used as an alternative model. From this paper, software developers have to consider the growth model by prior knowledge of the software to identify failure modes which can was helped.

A mathematical spatial interpolation method for the estimation of convective rainfall distribution over small watersheds

  • Zhang, Shengtang;Zhang, Jingzhou;Liu, Yin;Liu, Yuanchen
    • Environmental Engineering Research
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    • v.21 no.3
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    • pp.226-232
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    • 2016
  • Rainfall is one of crucial factors that impact on our environment. Rainfall data is important in water resources management, flood forecasting, and designing hydraulic structures. However, it is not available in some rural watersheds without rain gauges. Thus, effective ways of interpolating the available records are needed. Despite many widely used spatial interpolation methods, few studies have investigated rainfall center characteristics. Based on the theory that the spatial distribution of convective rainfall event has a definite center with maximum rainfall, we present a mathematical interpolation method to estimate convective rainfall distribution and indicate the rainfall center location and the center rainfall volume. We apply the method to estimate three convective rainfall events in Santa Catalina Island where reliable hydrological data is available. A cross-validation technique is used to evaluate the method. The result shows that the method will suffer from high relative error in two situations: 1) when estimating the minimum rainfall and 2) when estimating an external site. For all other situations, the method's performance is reasonable and acceptable. Since the method is based on a continuous function, it can provide distributed rainfall data for distributed hydrological model sand indicate statistical characteristics of given areas via mathematical calculation.

Estimation of weibull parameters for wind energy application in Iran's cities

  • Sedghi, Majid;Hannani, Siamak K.;Boroushaki, Mehrdad
    • Wind and Structures
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    • v.21 no.2
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    • pp.203-221
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    • 2015
  • Wind speed is the most important parameter in the design and study of wind energy conversion systems. The weibull distribution is commonly used for wind energy analysis as it can represent the wind variations with an acceptable level of accuracy. In this study, the wind data for 11 cities in Iran have been analysed over a period of one year. The Goodness of fit test is used for testing data fit to weibull distribution. The results show that this data fit to weibull function very well. The scale and shape factors are two parameters of the weibull distribution that depend on the area under study. The kinds of numerical methods commonly used for estimating weibull parameters are reviewed. Their performance for the cities under study was compared according to root mean square and wind energy errors. The result of the study reveals the empirical, modified maximum likelihood estimate of wind speed with minimum error. Also, that the moment and modified maximum likelihood are the best methods for estimating the energy production of wind turbines.

The Study for NHPP Software Reliability Growth Model Based on Hyper-exponential Distribution (초지수분포(Hyper-exponential)를 이용한 소프트웨어 신뢰성장 모형에 관한 연구)

  • Kim, Hee-Cheul;Shin, Hyun-Cheul
    • Convergence Security Journal
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    • v.7 no.1
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    • pp.45-53
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    • 2007
  • Finite failure NHPP models presented in the literature exhibit either constant, monotonic increasing or monotonic decreasing failure occurrence rates per fault. In this paper, Goel-Okumoto and Yamada-Ohba-Osaki model was reviewed, proposes the hyper-exponential distribution reliability model, which maked out efficiency application for software reliability. Algorithm to estimate the parameters used to maximum likelihood estimator and bisection method. For model determination and selection, explored goodness of fit (the error sum of squares). The methodology developed in this paper is exemplified with a software reliability random data set introduced by of Weibull distribution (shape 0.1 & scale 1) of Minitab (version 14) statistical package.

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