• Title/Summary/Keyword: Least Squares method

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Statistical review and explanation for Lanchester model (란체스터 모형에 대한 통계적 고찰과 해석)

  • Yoo, Byung Joo
    • The Korean Journal of Applied Statistics
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    • v.33 no.3
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    • pp.335-345
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    • 2020
  • This paper deals with the problem of estimating the log-transformed linear regression model to fit actual battle data from the Ardennes Campaign of World War II into the Lanchester model. The problem of determining a global solution for parameters and multicollinearity problems are identified and modified by examining the results of previous studies on data. The least squares method requires attention because a local solution can be found rather than a global solution if considering a specific constraint or a limited candidate group. The method of exploring this multicollinearity problem can be confirmed by a statistic known as a variance inflation factor. Therefore, the Lanchester model is simplified to avoid these problems, and the combat power attrition rate model was proposed which is statistically significant and easy to explain. When fitting the model, the dependence problem between the data has occurred due to autocorrelation. Matters that might be underestimated or overestimated were resolved by the Cochrane-Orcutt method as well as guaranteeing independence and normality.

Size selectivity of gill net for male snow crab, Chionoecetes opilio (자망에 대한 대게 수컷의 망목 선택성)

  • 박창두;안희춘;조삼광;백철인
    • Journal of the Korean Society of Fisheries and Ocean Technology
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    • v.39 no.2
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    • pp.143-151
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    • 2003
  • A series of fishing experiments was carried out in the waters off the east coast of Korea from January, 2002 to March, 2003, using gill nets of different mesh sizes (m = 180, 210, 240, 270, and 300 ㎜) to determine the size selectivity of gill net for male snow crab Chionoecetes opilio. The maximum carapace length (RL) of each male snow crab caught in the fishing experiment was measured. The master curve of mesh selectivity was estimated by applying the extended Kitahara's method. Two kinds of functional models, quadratic function and cubic function were used to express logarithmic selectivity curve and were fitted to the data using the method of least squares. The obtained results were summarized as follows; 1. The cubic function of asymmetry was chosen to determine the selectivity curve of gill net for male snow crab from the model deviance comparison. 2. The result of size selectivity showed that the catch number of small male crab was getting decreased according to the increase of mesh size. 3. The optimum value (RL/m) was 0.549 and the RL/m was estimated to be 0.281, 0.296, and 0.356 when the retention probability were 0.2, 0.25 and 0.5, respectively.

Prediction of the Chemical Composition and Fermentation Parameters of Fresh Coarse Italian Ryegrass Haylage using Near Infrared Spectroscopy

  • Kim, Ji Hye;Park, Hyung Soo;Choi, Ki Choon;Lee, Sang Hoon;Lee, Ki-Won
    • Journal of The Korean Society of Grassland and Forage Science
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    • v.37 no.4
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    • pp.350-357
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    • 2017
  • Near infrared spectroscopy (NIRS) is a rapid and accurate method for analyzing the quality of cereals, and dried animal forage. However, one limitation of this method is its inability to measure fermentation parameters in dried and ground samples because they are volatile, and therefore, respectively lost during the drying process. In order to overcome this limitation, in this study, fresh coarse haylage was used to test the potential of NIRS to accurately determine chemical composition and fermentation parameters. Fresh coarse Italian ryegrass haylage samples were scanned at 1 nm intervals over a wavelength range of 680 to 2500 nm, and optical data were recorded as log 1/reflectance. Spectral data, together with first- and second-order derivatives, were analyzed using partial least squares (PLS) multivariate regressions; scatter correction procedures (standard normal variate and detrend) were used in order to reduce the effect of extraneous noise. Optimum calibrations were selected based on their low standard error of cross validation (SECV) values. Further, ratio of performance deviation, obtained by dividing the standard deviation of reference values by SECV values, was used to evaluate the reliability of predictive models. Our results showed that the NIRS method can predict chemical constituents accurately (correlation coefficient of cross validation, $R_{cv}^2$, ranged from 0.76 to 0.97); the exception to this result was crude ash ($R_{cv}^2=0.49$ and RPD = 2.09). Comparison of mathematical treatments for raw spectra showed that second-order derivatives yielded better predictions than first-order derivatives. The best mathematical treatment for DM, ADF, and NDF, respectively was 2, 16, 16, whereas the best mathematical treatment for CP and crude ash, respectively was 2, 8, 8. The calibration models for fermentation parameters had low predictive accuracy for acetic, propionic, and butyric acids (RPD < 2.5). However, pH, and lactic and total acids were predicted with considerable accuracy ($R_{cv}^2$ 0.73 to 0.78; RPD values exceeded 2.5), and the best mathematical treatment for them was 1, 8, 8. Our findings show that, when fresh haylage is used, NIRS-based calibrations are reliable for the prediction of haylage characteristics, and therefore useful for the assessment of the forage quality.

A Method of Feature Extraction on Motor Imagery EEG Using FLD and PCA Based on Sub-Band CSP (서브 밴드 CSP기반 FLD 및 PCA를 이용한 동작 상상 EEG 특징 추출 방법 연구)

  • Park, Sang-Hoon;Lee, Sang-Goog
    • Journal of KIISE
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    • v.42 no.12
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    • pp.1535-1543
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    • 2015
  • The brain-computer interface obtains a user's electroencephalogram as a replacement communication unit for the disabled such that the user is able to control machines by simply thinking instead of using hands or feet. In this paper, we propose a feature extraction method based on a non-selected filter by SBCSP to classify motor imagery EEG. First, we divide frequencies (4~40 Hz) into 4-Hz units and apply CSP to each Unit. Second, we obtain the FLD score vector by combining FLD results. Finally, the FLD score vector is projected onto the optimal plane for classification using PCA. We use BCI Competition III dataset IVa, and Extracted features are used as input for LS-SVM. The classification accuracy of the proposed method was evaluated using $10{\times}10$ fold cross-validation. For subjects 'aa', 'al', 'av', 'aw', and 'ay', results were $85.29{\pm}0.93%$, $95.43{\pm}0.57%$, $72.57{\pm}2.37%$, $91.82{\pm}1.38%$, and $93.50{\pm}0.69%$, respectively.

Electrical Impedance Tomography for Material Profile Reconstruction of Concrete Structures (콘크리트 구조의 재료 물성 재구성을 위한 전기 임피던스 단층촬영 기법)

  • Jung, Bong-Gu;Kim, Boyoung;Kang, Jun Won;Hwang, Jin-Ha
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.32 no.4
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    • pp.249-256
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    • 2019
  • This paper presents an optimization framework of electrical impedance tomography for characterizing electrical conductivity profiles of concrete structures in two dimensions. The framework utilizes a partial-differential-equation(PDE)-constrained optimization approach that can obtain the spatial distribution of electrical conductivity using measured electrical potentials from several electrodes located on the boundary of the concrete domain. The forward problem is formulated based on a complete electrode model(CEM) for the electrical potential of a medium due to current input. The CEM consists of a Laplace equation for electrical potential and boundary conditions to represent the current inputs to the electrodes on the surface. To validate the forward solution, electrical potential calculated by the finite element method is compared with that obtained using TCAD software. The PDE-constrained optimization approach seeks the optimal values of electrical conductivity on the domain of investigation while minimizing the Lagrangian function. The Lagrangian consists of least-squares objective functional and regularization terms augmented by the weak imposition of the governing equation and boundary conditions via Lagrange multipliers. Enforcing the stationarity of the Lagrangian leads to the Karush-Kuhn-Tucker condition to obtain an optimal solution for electrical conductivity within the target medium. Numerical inversion results are reported showing the reconstruction of the electrical conductivity profile of a concrete specimen in two dimensions.

Simultaneous determination and difference evaluation of 14 ginsenosides in Panax ginseng roots cultivated in different areas and ages by high-performance liquid chromatography coupled with triple quadrupole mass spectrometer in the multiple reaction-monitoring mode combined with multivariate statistical analysis

  • Xiu, Yang;Li, Xue;Sun, Xiuli;Xiao, Dan;Miao, Rui;Zhao, Huanxi;Liu, Shuying
    • Journal of Ginseng Research
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    • v.43 no.4
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    • pp.508-516
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    • 2019
  • Background: Ginsenosides are not only the principal bioactive components but also the important indexes to the quality assessment of Panax ginseng Meyer. Their contents in cultivated ginseng vary with the growth environment and age. The present study aimed at evaluating the significant difference between 36 cultivated ginseng of different cultivation areas and ages based on the simultaneously determined contents of 14 ginsenosides. Methods: A high-performance liquid chromatography (HPLC) coupled with triple quadrupole mass spectrometer (MS) method was developed and used in the multiple reaction-monitoring (MRM) mode (HPLC-MRM/MS) for the quantitative analysis of ginsenosides. Multivariate statistical analysis, such as principal component analysis and partial least squares-discriminant analysis, was applied to discriminate ginseng samples of various cultivation areas and ages and to discover the differentially accumulated ginsenoside markers. Results: The developed HPLC-MRM/MS method was validated to be precise, accurate, stable, sensitive, and repeatable for the simultaneous determination of 14 ginsenosides. It was found that the 3- and 5-yr-old ginseng samples were differentiated distinctly by all means of multivariate statistical analysis, whereas the 4-yr-old samples exhibited similarity to either 3- or 5-yr-old samples in the contents of ginsenosides. Among the 14 detected ginsenosides, Rg1, Rb1, Rb2, Rc, 20(S)-Rf, 20(S)-Rh1, and Rb3 were identified as potential markers for the differentiation of cultivation ages. In addition, the 5-yr-old samples were able to be classified in cultivation area based on the contents of ginsenosides, whereas the 3- and 4-yr-old samples showed little differences in cultivation area. Conclusion: This study demonstrated that the HPLC-MRM/MS method combined with multivariate statistical analysis provides deep insight into the accumulation characteristics of ginsenosides and could be used to differentiate ginseng that are cultivated in different areas and ages.

Formation Estimation of Shaly Sandstone Reservoir using Joint Inversion from Well Logging Data (복합역산을 이용한 물리검층자료로부터의 셰일성 사암 저류층의 지층 평가)

  • Choi, Yeonjin;Chung, Woo-Keen;Ha, Jiho;Shin, Sung-ryul
    • Geophysics and Geophysical Exploration
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    • v.22 no.1
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    • pp.1-11
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    • 2019
  • Well logging technologies are used to measure the physical properties of reservoirs through boreholes. These technologies have been utilized to understand reservoir characteristics, such as porosity, fluid saturation, etc., using equations based on rock physics models. The analysis of well logs is performed by selecting a reliable rock physics model adequate for reservoir conditions or characteristics, comparing the results using the Archie's equation or simandoux method, and determining the most feasible reservoir properties. In this study, we developed a joint inversion algorithm to estimate physical properties in shaly sandstone reservoirs based on the pre-existing algorithm for sandstone reservoirs. For this purpose, we proposed a rock physics model with respect to shale volume, constructed the Jacobian matrix, and performed the sensitivity analysis for understanding the relationship between well-logging data and rock properties. The joint inversion algorithm was implemented by adopting the least-squares method using probabilistic approach. The developed algorithm was applied to the well-logging data obtained from the Colony gas sandstone reservoir. The results were compared with the simandox method and the joint inversion algorithms of sand stone reservoirs.

Establishment of a Nondestructive Analysis Method for Lignan Content in Sesame using Near Infrared Reflectance Spectroscopy (근적외선분광(NIRS)을 이용한 참깨의 lignan 함량 비파괴 분석 방법 확립)

  • Lee, Jeongeun;Kim, Sung-Up;Lee, Myoung-Hee;Kim, Jung-In;Oh, Eun-Young;Kim, Sang-Woo;Kim, MinYoung;Park, Jae-Eun;Cho, Kwang-Soo;Oh, Ki-Won
    • KOREAN JOURNAL OF CROP SCIENCE
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    • v.67 no.1
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    • pp.61-66
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    • 2022
  • Sesamin and sesamolin are major lignan components with a wide range of potential biological activities of sesame seeds. Near infrared reflectance spectroscopy (NIRS) is a rapid and non-destructive analysis method widely used for the quantitative determination of major components in many agricultural products. This study was conducted to develop a screening method to determine the lignan contents for sesame breeding. Sesamin and sesamolin contents of 482 sesame samples ranged from 0.03-14.40 mg/g and 0.10-3.79 mg/g with an average of 4.93 mg/g and 1.74 mg/g, respectively. Each sample was scanned using NIRS and calculated for the calibration and validation equations. The optimal performance calibration model was obtained from the original spectra using partial least squares (PLS). The coefficient of determination in calibration (R2) and standard error of calibration (SEC) were 0.963 and 0.861 for sesamin and 0.875 and 0.292 for sesamolin, respectively. Cross-validation results of the NIRS equation showed an R2 of 0.889 in the prediction for sesamin and 0.781 for sesamolin and a standard error of cross-validation (SECV) of 1.163 for sesamin and 0.417 for sesamolin. The results showed that the NIRS equation for sesamin and sesamolin could be effective in selecting high lignan sesame lines in early generations of sesame breeding.

Discrimination of the drinking water taste by potentiometric electronic tongue and multivariate analysis (전자혀 및 다변량 분석법을 활용한 먹는물의 구별 방법)

  • Eunju Kim;Tae-Mun Hwang;Jae-Wuk Koo;Jaeyong Song;Hongkyeong Park;Sookhyun Nam
    • Journal of Korean Society of Water and Wastewater
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    • v.37 no.6
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    • pp.425-435
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    • 2023
  • Organoleptic parameters such as color, odor, and flavor influence consumer perception of drinking water quality. This study aims to evaluate the taste of the selected bottled and tap water samples using an electronic tongue (E-tongue) instead of a sensory test. Bottled and tap water's mineral components are related to the overall preference for water taste. Contrary to the sensory test, the potentiometric E-tongue method presented in this study distinguishes taste by measuring the mineral components in water, and the data obtained can be statistically analyzed. Eleven bottled water products from various brands and one tap water from I city in Korea were evaluated. The E-tongue data were statistically analyzed using multivariate statistical tools such as hierarchical clustering analysis (HCA), principal component analysis (PCA), and partial least squares discriminant analysis (PLS-DA). The results show that the E-tongue method can clearly distinguish taste discrimination in drinking water differing in water quality based on the ion-related water quality parameters. The water quality parameters that affect taste discrimination were found to be total dissolved solids (TDS), sodium (Na+), calcium (Ca2+), magnesium (Mg2+), sulfate (SO42-), chloride (Cl-), potassium (K+) and pH. The distance calculation of HCA was used to quantify the differences between 12 different types of drinking water. The proposed E-tongue method is a practical tool to quantitatively evaluate the differences between samples in water quality items related to the ionic components. It can be helpful in quality control of drinking water.

Design of 10bit gamma line system with small size of gate count and 4bit error(LSB) to implement non-linear gamma curve (비선형 감마 커브 구현을 위한 작은 크기와 4bit(LSB) 오차를 가진 10비트 감마 라인 시스템의 설계)

  • Jang, Won-Woo;Kim, Hyun-Sik;Lee, Sung-Mok;Kim, In-Kyu;Kang, Bong-Soon
    • Proceedings of the Korea Institute of Convergence Signal Processing
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    • 2005.11a
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    • pp.353-356
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    • 2005
  • In this paper, the proposed $gamma({\gamma})$ line system is developed for reducing the error between non-linear gamma curve produced by a formula and result produced by hardware implementation. The proposed algorithm and system is based on the specific gamma value 2.2, namely the formula is represented by {0,1}$^{2.2}$ and the bit width of input and out data is 10bit. In order to reduce the error, the system is using least squares polynomial of the numerical method which is calculating the best fitting polynomial through a set of points. The proposed gamma line is consisting of nine kinds of quadratic equations, each with their own overlap sections to get more precise. Based on the algorithm verified by $MATLAB^{TM}$ 7.0, the proposed system is implemented by using Verilog-HDL. The proposed system has 2 clock latency; 1 result per clock. The error range (LSB) is -4 and +3. Its standard deviation is 1.287956238. The total gate count of system is 2,083 gates and the maximum timing is 15.56[ns].

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