• Title/Summary/Keyword: 최소 자승 오차법

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Prediction on Mix Proportion Factor and Strength of Concrete Using Neural Network (신경망을 이용한 콘크리트 배합요소 및 압축강도 추정)

  • 김인수;이종헌;양동석;박선규
    • Journal of the Korea Concrete Institute
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    • v.14 no.4
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    • pp.457-466
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    • 2002
  • An artificial neural network was applied to predict compressive strength, slump value and mix proportion of a concrete. Standard mixed tables were trained and estimated, and the results were compared with those of the experiments. To consider variabilities of material properties, the standard mixed fables from two companies of Ready Mixed Concrete were used. And they were trained with the neural network. In this paper, standard back propagation network was used. The mix proportion factors such as water cement ratio, sand aggregate ratio, unit water, unit cement, unit weight of sand, unit weight of crushed sand, unit coarse aggregate and air entraining admixture were used. For the arrangement on the approval of prediction of mix proportion factor, the standard compressive strength of $180kgf/cm^2{\sim}300kgf/cm^2$, and target slump value of 8 cm, 15 cm were used. For the arrangement on the approval of prediction of compressive strength and slump value, the standard compressive strength of $210kgf/cm^2{\sim}240kgf/cm^2$, and target slump value of 12 cm and 15 cm wore used because these ranges are most frequently used. In results, in the prediction of mix proportion factor, for all of the water cement ratio, sand aggregate ratio, unit water, unit cement, unit weight of sand, unit weight of crushed sand, unit coarse aggregate, air entraining admixture, the predicted values and the values of standard mixed tables were almost the same within the target error of 0.10 and 0.05, regardless of two companies. And in the prediction of compressive strength and slump value, the predicted values were converged well to the values of standard mixed fables within the target error of 0.10, 0.05, 0.001. Finally artificial neural network is successfully applied to the prediction of concrete mixture and compressive strength.

Crystal Structures of Fully Dehydrated $Ca^{2+}$-Exchanged Zeolite X, $Ca_{46}-X$, and $Ca^{2+}$ and $K^+$-Exchanged Zeolite X, $Ca_{32}K_{28}-X$ ($Ca^{2+}$ 이온으로 완전히 치환된 제올라이트 X, $Ca_{46}-X$$Ca^{2+}$ 이온과 $K^+$ 이온으로 치환된 제올라이트 X, $Ca_{32}K_{28}-X$를 완전히 진공 탈수한 결정구조)

  • Jang, Se Bok;Song, Seong Hwan;Kim, Yang
    • Journal of the Korean Chemical Society
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    • v.39 no.1
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    • pp.7-13
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    • 1995
  • The crystal sructures of $X(Ca_{46}Al_{92}Si_{100}O_{384})$ and $Ca_{32}K_{28}-X(Ca_{32}K_{28}Al_{92}Si_{100}O_{384})$ dehydrated at $360^{\circ}C$ and $2{\times}10^{-6}$ Torr have been determined by single-crystal X-ray diffraction techniques in the cubic space group Fd3 at $21(1)^{\circ}C.$ Their structures were refined to the final error indices, R_1=0.096,\;and\;R_2=0.068$ with 166 reflections, and R_1=0.078\;and\;R_2=0.056$ with 130 reflections, respectively, for which I > $3\sigma(I).$ In dehydrated $Ca_{48}-X,\;Ca^{2+}$ ions are located at two different sites opf high occupancies. Sixteen $Ca^{2+}$ ions are located at site I, the centers of the double six rings $(Ca(1)-O(3)=2.51(2)\AA$ and thirty $Ca^{2+}$ ions are located at site II, the six-membered ring faces of sodalite units in the supercage. Latter $Ca^{2+}$ ions are recessed $0.44\AA$ into the supercage from the three O(2) oxygen plane (Ca(2)-O(2)= $2.24(2)\AA$ and $O(2)-Ca(2)-O(2)=119(l)^{\circ}).$ In the structure of $Ca_{32}K_{28}-X$, all $Ca^{2+}$ ions and $K^+$ ions are located at the four different crystallographic sites: 16 $Ca^{2+}$ ions are located in the centers of the double six rings, another sixteen $Ca^{2+}$ ions and sixteen $K^+$ ions are located at the site II in the supercage. These $Ca^{2+}$ ions adn $K^+$ ions are recessed $0.56\AA$ and $1.54\AA$, respectively, into the supercage from their three O(2) oxygen planes $(Ca(2)-O(2)=2.29(2)\AA$, $O(2)-Ca(2)-O(2)=119(1)^{\circ}$, $K(1)-O(2)=2.59(2)\AA$, and $O(2)-K(1)-O(2)=99.2(8)^{\circ}).$ Twelve $K^+$ ions lie at the site III, twofold axis of edge of the four-membered ring ladders inside the supercage $(K(2)-O(4)=3.11(6)\AA$ and $O(1)-K(2)-O(1)=128(2)^{\circ}).$

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Three Crystal Structures of Dehydrated Partially $Co^{2+}-Exchanged$ Zeolite A Treated with Potassium Vapor (부분적으로 코발트 이온으로 치환한 제올라이트 A를 진공 탈수한 후 칼륨 증기로 반응시킨 3개의 결정구조)

  • Jeong Mi Suk;Jang Se Bok
    • Korean Journal of Crystallography
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    • v.15 no.2
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    • pp.59-68
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    • 2004
  • Three crystal structures of dehydrated partially $Co^{2+}-exchanged$ zeolite A treated with 0.6 Torr of K at $300^{\circ}C$ (for 12 hrs, 6 hrs, and 2 hrs) vapor have been determined by single-crystal X-ray diffraction techniques in the cubic space group Pm3m at 21(1)$^{\circ}C(a=12.181(1)\;{\AA},\;a=12.184(1)\;{\AA},\;and\;a=12.215(1)\;{\AA})\;respectively)$. Their structures were refined to the final error indices, R(weight) of 0.090 with 10 reflections, 0.091 with 82 reflections, and 0.090 with 80 reflections, respectively, for which $1>\sigma(I)$. In each structure, all four $Co^{2+}$ and four $Na^+$ ions to be reduced by K atoms. The cobalt and sodium atoms produced are no longer found in the zeolite. K species are found at five different crystallographic sites: three $K^+$ ions lie at the planes of 8-rings, filling that position, ca. 11.5 K^+$ ions lie on threefold axes, ca. 4.0 in the large cavity and ca. 4.0 in the sodalite cavity, and ca. 0.5 $K^+$ ion is found near a 4-ring. ca. three $K^0$ atoms are found deep into the large cavity on threefold axes. In these structures, crystallographic results show that cationic tetrahedral $K_4$ (and/or triangular $K_3$) clusters have formed in the sodalites of zeolite A. The $K_4$ and/or $K_3$ clusters coordinate trigonally to three oxygens of a six-oxygen ring. The partially reduced ions of these clusters interact primarily with oxygen atoms of the zeolite structure rather than with each other. ca. 14.5K species are found per unit cell, more than the twelve $K^+$ ions needed to balance the anionic charge of zeolite framework, indicating that sorption of $K^0$ has occurred. The three $K^0$ atoms in the large cavity are closely associated with three out of four $K^+$ ions in the large cavity to form $K_7^{4+}$ clusters. The $K_7^{4+}$ cluster not interacts primarily with framework oxygens.

The Cross-Sectional Characteristic and Spring-Neap Variation of Residual Current and Net Volume Transport at the Yeomha Channel (경기만 염하수로에서의 잔차류 및 수송량의 대조-소조 변동과 단면 특성)

  • Lee, Dong Hwan;Yoon, Byung Il;Woo, Seung-Buhm
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.29 no.5
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    • pp.217-227
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    • 2017
  • The object of this study is to estimate the net volume transport and the residual flow that changed by space and time at southern part of Yeomha channel, Gyeonggi Bay. The cross-section observation was conducted at the mid-part (Line2) and the southern end (Line1) of Yeomha channel for 13 hours during neap and spring-tides, respectively. The Lagrange flux is calculated as the sum of Eulerian flux and Stokes drift, and the residual flow is calculated by using least square method. It is necessary to unify the spatial area of the observed cross-section and average time during the tidal cycle. In order to unify the cross-sectional area containing such a large vertical tidal variation, it was necessary to convert into sigma coordinate system by horizontally and vertically for every hour. The converted sigma coordinate system is estimated to be 3~5% error when compared with the z-level coordinate system which shows that there is no problem for analyzing the data. As a result, the cross-sectional residual flow shows a southward flow pattern in both spring and neap tides at Line2, and also have characteristic of the spatial residual flow fluctuation: it northwards in the main line direction and southwards at the end of both side of the waterway. It was confirmed that the residual flow characteristics at Line2 were changed by the net pressure due to the sea level difference. The analysis of the net volume transport showed that it tends to southwards at $576m^3s^{-1}$, $67m^3s^{-1}$ in each spring tide and neap tide at Line2. On the other hand, in the control Line1, it has tendency to northwards at $359m^3s^{-1}$ and $248m^3s^{-1}$. Based on the difference between the two observation lines, it is estimated that net volume transport will be out flow about $935m^3s^{-1}$ at spring tide stage and about $315m^3s^{-1}$ at neap tide stage as the intertidal zone between Yeongjong Island and Ganghwa Island. In other words, the difference of pressure gradient and Stokes drift during spring and neap tide is main causes of variation for residual current and net volume transport.

Three Crystal Structures of Dehydrated $Ag_{12-x}Na_x-A$ (x = 4, 6, and 8) Treated with Rubidium Vapor (탈수한 $Ag_{12-x}Na_x-A$ (x = 4, 6, 및 8)를 루비듐 증기로 처리한 세가지 결정구조)

  • Lee, Hyeon Do;Kim, Un Sik;Park, Jong Yeol;Kim, Yang
    • Journal of the Korean Chemical Society
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    • v.38 no.3
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    • pp.186-196
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    • 1994
  • Three fully dehydrated partially $Ag^+$-exchanged zeolite A(Ag_4Na_8-A, Ag_6Na_6-A, and Ag_8Na_4-A) were treated at $250^{\circ}C$ with 0.1 torr Rb vapor at 4 h. Their structures were determined by singlecrystal X-ray diffraction methods in the cubic space group $Pm{\bar3}m$ (a = 12.264(4) $\AA$, a = 12.269(1) $\AA$, and a= 12.332(3) $\AA$, respectively) at $22(1)^{\circ}C$, and were refined to the final error indices, R(weighed), of 0.056 with 131 reflections, 0.068 with 108 reflections, and 0.070 with 94 reflections, respectively, for which I > $3\sigma(I).$ In these structures, Rb species are found at three different crystallographic sites; three $Rb^+$ ions per unit cell are located at 8-ring centers, ca. 6.0∼6.8 $Rb^+$ ions are found opposite 6-rings on threefold axes in the large cavity, and ca. 2.5 $Rb^+$ ions are found on three fold axes in the sodalite unit. Also, Ag species are found at two different crystallographic sites; ca. 0.6∼1.0 $Ag^+$ ion lies opposite 4-rings and about 1.8∼4.2 Ag atoms are located near the center of the large cavity. In these structures, the numbers of Ag atoms per unit cell are 1.8, 3.0, and 4.2, respectively, and these are likely to form hexasilver clusters at the centers of the large cavities. The $Rb^+$ ions, by blocking 8-rings, may have prevented silver atoms from migrating out of the structure. Each hexasilver cluster is stabilized by coordination to 6-ring, 8-ring $Rb^+$ ions, and also by coordination to a 4-ring $Ag^+$ ion.

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Crystal Structures of $Cd_6-A$ Dehydrated at $750^{\circ}C$ and Dehydrated $Cd_6-A$ Reacted with Cs Vapor ($750^{\circ}C$ 에서 탈수한 $Cd_6-A$의 결정구조와 이 결정을 세슘 증기로 반응시킨 결정구조)

  • Se Bok Jang;Yang Kim
    • Journal of the Korean Chemical Society
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    • v.37 no.2
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    • pp.191-198
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    • 1993
  • The crystal structures of $Cd_{6-}A$ evacuated at $2{\times}10^{-6}$ torr and $750^{\circ}C$ (a = 12.204(1) $\AA$) and dehydrated $Cd_{6-}A$ reacted with 0.1 torr of Cs vapor at $250^{\circ}C$ for 12 hours (a = 12.279(1) $\AA$) have been determined by single crystal X-ray diffraction techniques in the cubic space group Pm3m at $21(1)^{\circ}C.$ Their structures were refined to final error indices, $R_1=$ 0.081 and $R_2=$ 0.091 with 151 reflections and $R_1=$ 0.095 and $R_2=$ 0.089 with 82 reflections, respectively, for which I > $3\sigma(I).$ In vacuum dehydrated $Cd_{6-}A$, six $Cd^{2+}$ ions occupy threefold-axis positions near 6-ring, recessed 0.460(3) $\AA$ into the sodalite cavity from the (111) plane at O(3) : Cd-O(3) = 2.18(2) $\AA$ and O(3)-Cd-O(3) = $115.7(4)^{\circ}.$ Upon treating it with 0.1 torr of Cs vapor at $250^{\circ}C$, all 6 $Cd^{2+}$ ions in dehydrated $Cd_{6-}A$ are reduced by Cs vapor and Cs species are found at 4 crystallographic sites : 3.0 $Cs^+$ ions lie at the centers of the 8-rings at sites of $D_{4h}$ symmetry; ca. 9.0 Cs+ ions lie on the threefold axes of unit cell, ca. 7 in the large cavity and ca. 2 in the sodalite cavity; ca. 0.5 $Cs^+$ ion is found near a 4-ring. In this structure, ca. 12.5 Cs species are found per unit cell, more than the twelve $Cs^+$ ions needed to balance the anionic charge of zeolite framework, indicating that sorption of Cs0 has occurred. The occupancies observed are simply explained by two unit cell arrangements, $Cs_{12}-A$ and $Cs_{13}-A$. About 50% of unit cells may have two $Cs^+$ ions in sodalite unit near opposite 6-rings, six in the large cavity near 6-ring and one in the large cavity near a 4-ring. The remaining 50% of unit cells may have two Cs species in the sodalite unit which are closely associated with two out of 8 $Cs^+$ ions in the large cavity to form linear $(Cs_4)^{3+}$ clusters. These clusters lie on threefold axes and extend through the centers of sodalite units. In all unit cells, three $Cs^+$ ions fill equipoints of symmetry $D_{4h}$ at the centers of 8-rings.

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Crystal Structures of Full Dehydrated $Ca_{35}Cs_{22}Si_{100}Al_{92}O_{384}$and $Ca_{29}Cs_{34}Si_{100}Al_{92}O_{384}$ ($Ca^{2+}$ 이온과 $Cs^+$ 이온으로 치환되고 탈수된 두개의 제올라이트 X $Ca_{35}Cs_{22}Si_{100}Al_{92}O_{384}$$Ca_{29}Cs_{34}Si_{100}Al_{92}O_{384}$의 결정구조)

  • Jang, Se Bok;Song, Seung Hwan;Kim, Yang
    • Journal of the Korean Chemical Society
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    • v.40 no.6
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    • pp.427-435
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    • 1996
  • The structures of fully dehydrated $Ca^{2+}$- and $Cs^+$-exchanged zeolite X, $Ca_{35}Cs_{22}Si_{100}Al_{92}O_{384}$($Ca_{35}Cs_{22}$-X; a=25.071(1) $\AA)$ and $Ca_{29}Cs_{34}Si_{100}Al_{92}O_{384}$($Ca_{29}Cs_{34}$-X; a=24.949(1) $\AA)$, have been determined by single-crystal X-ray diffraction methods in the cubic space group Fd3 at $21(1)^{\circ}C.$ Their structures were refined to the final error indices $R_1$=0.051 and $R_2$=0.044 with 322 reflections for $Ca_{35}Cs_{22}$-X, and $R_1$=0.058 and $R_2$=0.055 with 260 reflections for $Ca_{29}Cs_{34}$-X; $I>3\sigma(I).$ In both structures, $Ca^{2+}$ and $Cs^+$ ions are located at five different crystallographic sites. In dehydrated $Ca_{35}Cs_{22}$-X, sixteen $Ca^{2+}$ ions fill site I, at the centers of the double 6-rings(Ca-O=2.41(1) $\AA$ and $O-Ca-O=93.4(3)^{\circ}).$ Another nineteen $Ca^{2+}$ ions occupy site II (Ca-O=2.29(1) $\AA$, O-Ca-O=118.7(4)') and ten $Cs^+$ ions occupy site II opposite single six-rings in the supercage; each is $1.95\AA$ from the plane of three oxygens (Cs-O=2.99(1) and $O-Cs-O=82.3(3)^{\circ}).$ About three $Cs^+$ ions are found at site II', 2.27 $\AA$ into sodalite cavity from their three-oxygen plane (Cs-O=3.23(1) $\AA$ and $O-Cs-O=75.2(3)^{\circ}).$ The remaining nine $Cs^+$ ions are statistically distributed over site Ⅲ, a 48-fold equipoint in the supercages on twofold axes (Cs-O=3.25(1) $\AA$ and Cs-O=3.49(1) $\AA).$ In dehydrated $Ca_{29}Cs_{34}$-X, sixteen $Ca^{2+}$ ions fill site I(Ca-O=2.38(1) $\AA$ and $O-Ca-O=94.1(4)^{\circ})$ and thirteen $Ca^{2+}$ ions occupy site II (Ca-O=2.32(2) $\AA$, $O-Ca-O=119.7(6)^{\circ}).$ Another twelve $Cs^+$ ions occupy site II; each is $1.93\AA$ from the plane of three oxygens (Cs-O=3.02(1) and $O-Cs-O=83.1(4)^{\circ})$ and seven $Cs^+$ ions occupy site II'; each is $2.22\AA$ into sodalite cavity from their three-oxygen plane (Cs-O=3.21(2) and $O-Cs-O=77.2(4)^{\circ}).$ The remaining sixteen $Cs^+$ ions are found at III site in the supercage (Cs-O=3.11(1) $\AA$ and Cs-O=3.46(2) $\AA).$ It appears that $Ca^{2+}$ ions prefer sites I and II in that order, and that $Cs^+$ ions occupy the remaining sites, except that they are too large to be stable at site I.

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Estimation of GARCH Models and Performance Analysis of Volatility Trading System using Support Vector Regression (Support Vector Regression을 이용한 GARCH 모형의 추정과 투자전략의 성과분석)

  • Kim, Sun Woong;Choi, Heung Sik
    • Journal of Intelligence and Information Systems
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    • v.23 no.2
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    • pp.107-122
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    • 2017
  • Volatility in the stock market returns is a measure of investment risk. It plays a central role in portfolio optimization, asset pricing and risk management as well as most theoretical financial models. Engle(1982) presented a pioneering paper on the stock market volatility that explains the time-variant characteristics embedded in the stock market return volatility. His model, Autoregressive Conditional Heteroscedasticity (ARCH), was generalized by Bollerslev(1986) as GARCH models. Empirical studies have shown that GARCH models describes well the fat-tailed return distributions and volatility clustering phenomenon appearing in stock prices. The parameters of the GARCH models are generally estimated by the maximum likelihood estimation (MLE) based on the standard normal density. But, since 1987 Black Monday, the stock market prices have become very complex and shown a lot of noisy terms. Recent studies start to apply artificial intelligent approach in estimating the GARCH parameters as a substitute for the MLE. The paper presents SVR-based GARCH process and compares with MLE-based GARCH process to estimate the parameters of GARCH models which are known to well forecast stock market volatility. Kernel functions used in SVR estimation process are linear, polynomial and radial. We analyzed the suggested models with KOSPI 200 Index. This index is constituted by 200 blue chip stocks listed in the Korea Exchange. We sampled KOSPI 200 daily closing values from 2010 to 2015. Sample observations are 1487 days. We used 1187 days to train the suggested GARCH models and the remaining 300 days were used as testing data. First, symmetric and asymmetric GARCH models are estimated by MLE. We forecasted KOSPI 200 Index return volatility and the statistical metric MSE shows better results for the asymmetric GARCH models such as E-GARCH or GJR-GARCH. This is consistent with the documented non-normal return distribution characteristics with fat-tail and leptokurtosis. Compared with MLE estimation process, SVR-based GARCH models outperform the MLE methodology in KOSPI 200 Index return volatility forecasting. Polynomial kernel function shows exceptionally lower forecasting accuracy. We suggested Intelligent Volatility Trading System (IVTS) that utilizes the forecasted volatility results. IVTS entry rules are as follows. If forecasted tomorrow volatility will increase then buy volatility today. If forecasted tomorrow volatility will decrease then sell volatility today. If forecasted volatility direction does not change we hold the existing buy or sell positions. IVTS is assumed to buy and sell historical volatility values. This is somewhat unreal because we cannot trade historical volatility values themselves. But our simulation results are meaningful since the Korea Exchange introduced volatility futures contract that traders can trade since November 2014. The trading systems with SVR-based GARCH models show higher returns than MLE-based GARCH in the testing period. And trading profitable percentages of MLE-based GARCH IVTS models range from 47.5% to 50.0%, trading profitable percentages of SVR-based GARCH IVTS models range from 51.8% to 59.7%. MLE-based symmetric S-GARCH shows +150.2% return and SVR-based symmetric S-GARCH shows +526.4% return. MLE-based asymmetric E-GARCH shows -72% return and SVR-based asymmetric E-GARCH shows +245.6% return. MLE-based asymmetric GJR-GARCH shows -98.7% return and SVR-based asymmetric GJR-GARCH shows +126.3% return. Linear kernel function shows higher trading returns than radial kernel function. Best performance of SVR-based IVTS is +526.4% and that of MLE-based IVTS is +150.2%. SVR-based GARCH IVTS shows higher trading frequency. This study has some limitations. Our models are solely based on SVR. Other artificial intelligence models are needed to search for better performance. We do not consider costs incurred in the trading process including brokerage commissions and slippage costs. IVTS trading performance is unreal since we use historical volatility values as trading objects. The exact forecasting of stock market volatility is essential in the real trading as well as asset pricing models. Further studies on other machine learning-based GARCH models can give better information for the stock market investors.