• Title/Summary/Keyword: Non-linear Equation

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An efficient 2.5D inversion of loop-loop electromagnetic data (루프-루프 전자탐사자료의 효과적인 2.5차원 역산)

  • Song, Yoon-Ho;Kim, Jung-Ho
    • Geophysics and Geophysical Exploration
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    • v.11 no.1
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    • pp.68-77
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    • 2008
  • We have developed an inversion algorithm for loop-loop electromagnetic (EM) data, based on the localised non-linear or extended Born approximation to the solution of the 2.5D integral equation describing an EM scattering problem. Source and receiver configuration may be horizontal co-planar (HCP) or vertical co-planar (VCP). Both multi-frequency and multi-separation data can be incorporated. Our inversion code runs on a PC platform without heavy computational load. For the sake of stable and high-resolution performance of the inversion, we implemented an algorithm determining an optimum spatially varying Lagrangian multiplier as a function of sensitivity distribution, through parameter resolution matrix and Backus-Gilbert spread function analysis. Considering that the different source-receiver orientation characteristics cause inconsistent sensitivities to the resistivity structure in simultaneous inversion of HCP and VCP data, which affects the stability and resolution of the inversion result, we adapted a weighting scheme based on the variances of misfits between the measured and calculated datasets. The accuracy of the modelling code that we have developed has been proven over the frequency, conductivity, and geometric ranges typically used in a loop-loop EM system through comparison with 2.5D finite-element modelling results. We first applied the inversion to synthetic data, from a model with resistive as well as conductive inhomogeneities embedded in a homogeneous half-space, to validate its performance. Applying the inversion to field data and comparing the result with that of dc resistivity data, we conclude that the newly developed algorithm provides a reasonable image of the subsurface.

Age and Growth of Small Yellow Croaker, Larimichthys polyactis in the South Sea of Korea (한국 남해 참조기의 연령과 성장)

  • Kim, Yeong Hye;Lee, Sun Kil;Lee, Jae Bong;Lee, Dong Woo;Kim, Young Seop
    • Korean Journal of Ichthyology
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    • v.18 no.1
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    • pp.45-54
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    • 2006
  • Age and growth of the small yellow croaker, Larimichthys polyactis were estimated using right sagittal otoliths of 506 fish specimens from March to December, 2002 and from January to February, 2005 in the South Sea, part of the East China Sea of Korea. Examination of outer margins of the otolith showed that the opaque zone was formed once a year. Marginal increment of the otolith formed annual rings from May and June at the beginning of spawning season. In the relationship between total length and body weight, a multiplicative error structure was assumed because variability in growth increased as a function of the length, and the estimated equation was $BW=0.0044TL^{3.2502}$ ($R^2=0.97$). The relative growth as body weight at total length has significant difference between females and males (P<0.05). For describing growth of the small yellow croaker, Larimichthys polyactis a von Bertalanffy growth model was adopted. The von Bertalanffy growth curve had an additive error structure and the growth parameters estimated from non-linear regression were $L_{\infty}=33.88cm$, K=0.20/year and $t_0=-2.39year$. Growth at age of males and females shows no significant difference (P>0.05). Most examined fish were 1, 2 and 3 years old, although the oldest fish were 7 old for males and 8 for females.

Determination of CPT-based Bearing Capacity of Footings Under Surcharge Using State-dependent Finite Element Analysis (상태의존성 유한요소해석 및 CPT결과를 적용한 상재하중하의 얕은 기초의 지지력 결정)

  • Lee Jun-Hwan;Kim Dae-Ho;Park Dong-Gyu
    • Journal of the Korean Geotechnical Society
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    • v.21 no.7
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    • pp.55-62
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    • 2005
  • The use of the bearing capacity equation is subjected to several uncertainties. In this study, estimation of the bearing capacity of footings based on the cone resistance q$_{c}$ is investigated. Non-linear finite element analyses based on a state-dependent stress-strain model were performed to obtain the load-settlement responses of axially loaded circular footings. Various soil and footing conditions, including different relative densities, depths of embedment, and footing diameters were considered in the analyses. Based on the finite element results, load-settlement curves were obtained and used to determine the unit limit bearing capacity in terms of the cone resistance q$_{c}$ for footings subjected to surcharge. Values of the unit bearing capacity for different embedment depths were in a narrow range, while considerable variation was observed with relative density D$_{R}$. It was observed that the unit limit bearing capacity normalized with respect to q$_{c}$ decreases as D$_{R}$ increases for a given surcharge.

A Comparative Study On Accident Prediction Model Using Nonlinear Regression And Artificial Neural Network, Structural Equation for Rural 4-Legged Intersection (비선형 회귀분석, 인공신경망, 구조방정식을 이용한 지방부 4지 신호교차로 교통사고 예측모형 성능 비교 연구)

  • Oh, Ju Taek;Yun, Ilsoo;Hwang, Jeong Won;Han, Eum
    • Journal of Korean Society of Transportation
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    • v.32 no.3
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    • pp.266-279
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    • 2014
  • For the evaluation of roadway safety, diverse methods, including before-after studies, simple comparison using historic traffic accident data, methods based on experts' opinion or literature, have been applied. Especially, many research efforts have developed traffic accident prediction models in order to identify critical elements causing accidents and evaluate the level of safety. A traffic accident prediction model must secure predictability and transferability. By acquiring the predictability, the model can increase the accuracy in predicting the frequency of accidents qualitatively and quantitatively. By guaranteeing the transferability, the model can be used for other locations with acceptable accuracy. To this end, traffic accident prediction models using non-linear regression, artificial neural network, and structural equation were developed in this study. The predictability and transferability of three models were compared using a model development data set collected from 90 signalized intersections and a model validation data set from other 33 signalized intersections based on mean absolute deviation and mean squared prediction error. As a result of the comparison using the model development data set, the artificial neural network showed the highest predictability. However, the non-linear regression model was found out to be most appropriate in the comparison using the model validation data set. Conclusively, the artificial neural network has a strong ability in representing the relationship between the frequency of traffic accidents and traffic and road design elements. However, the predictability of the artificial neural network significantly decreased when the artificial neural network was applied to a new data which was not used in the model developing.

3D Modeling and Inversion of Magnetic Anomalies (자력이상 3차원 모델링 및 역산)

  • Cho, In-Ky;Kang, Hye-Jin;Lee, Keun-Soo;Ko, Kwang-Beom;Kim, Jong-Nam;You, Young-June;Han, Kyeong-Soo;Shin, Hong-Jun
    • Geophysics and Geophysical Exploration
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    • v.16 no.3
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    • pp.119-130
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    • 2013
  • We developed a method for inverting magnetic data to recover the 3D susceptibility models. The major difficulty in the inversion of the potential data is the non-uniqueness and the vast computing time. The insufficient number of data compared with that of inversion blocks intensifies the non-uniqueness problem. Furthermore, there is poor depth resolution inherent in magnetic data. To overcome this non-uniqueness problem, we propose a resolution model constraint that imposes large penalty on the model parameter with good resolution; on the other hand, small penalty on the model parameter with poor resolution. Using this model constraint, the model parameter with a poor resolution can be effectively resolved. Moreover, the wavelet transform and parallel solving were introduced to save the computing time. Through the wavelet transform, a large system matrix was transformed to a sparse matrix and solved by a parallel linear equation solver. This procedure is able to enormously save the computing time for the 3D inversion of magnetic data. The developed inversion algorithm is applied to the inversion of the synthetic data for typical models of magnetic anomalies and real airborne data obtained at the Geumsan area of Korea.

Estimation of Annual Energy Production Based on Regression Measure-Correlative-Predict at Handong, the Northeastern Jeju Island (제주도 북동부 한동지역의 MCP 회귀모델식을 적용한 AEP계산에 대한 연구)

  • Ko, Jung-Woo;Moon, Seo-Jeong;Lee, Byung-Gul
    • Journal of the Korean Society of Marine Environment & Safety
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    • v.18 no.6
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    • pp.545-550
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    • 2012
  • Wind resource assessment is necessary when designing wind farm. To get the assessment, we must use a long term(20 years) observed wind data but it is so hard. so that we usually measured more than a year on the planned site. From the wind data, we can calculate wind energy related with the wind farm site. However, it calculate wind energy to collect the long term data from Met-mast(Meteorology Mast) station on the site since the Met-mast is unstable from strong wind such as Typhoon or storm surge which is Non-periodic. To solve the lack of the long term data of the site, we usually derive new data from the long term observed data of AWS(Automatic Weather Station) around the wind farm area using mathematical interpolation method. The interpolation method is called MCP(Measure-Correlative-Predict). In this study, based on the MCP Regression Model proposed by us, we estimated the wind energy at Handong site using AEP(Annual Energy Production) from Gujwa AWS data in Jeju. The calculated wind energy at Handong was shown a good agreement between the predicted and the measured results based on the linear regression MCP. Short term AEP was about 7,475MW/year. Long term AEP was about 7,205MW/year. it showed an 3.6% of annual prediction different. It represents difference of 271MW in annual energy production. In comparison with 20years, it shows difference of 5,420MW, and this is about 9 months of energy production. From the results, we found that the proposed linear regression MCP method was very reasonable to estimate the wind resource of wind farm.

Estimation of Energy Budget from Food Consumption and Growth of Hexagrammos agrammus (노래미, Hexagrammos agrammus의 섭식양과 성장양으로부터 에너지 대사의 추정)

  • KIM Chong-Kwan;ZHANG Chang-Ik
    • Korean Journal of Fisheries and Aquatic Sciences
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    • v.31 no.1
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    • pp.121-126
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    • 1998
  • This study is to examine the energy budget of Hexagrammos agrammus in the natural habitat, based on the von Bertalanffy's growth model using food consumption and growth data of the fish. The fish were collected at the coasts of Tongbaek Island in Pusan and Shinsu Island in Samchonpo, Korea. The standard energy budget model was adopted for this study and the model has the components of toed consumption (C), production (G), assimilation (A), absorption ($A_b$), catabolism (R), excreta (U) and feces (F). These components were expressed as mass unit, not as calorie unit as usual. Both the mass and the proportion of each component varied with age of the fish, The mass of annual excreta declined as the fish became older, while those of the other components increased with the age. The relationship between mean weight (W) and annual absorption ($A_b$) was a non-linear one with the equation of $A_b=4.592W^{0.666}$, while that between mean weight (W) and annual catabolism (R) was linear as R=0.007+0.567W. On the other hand, the annual food consumption (C) showed linear relations both with annual assimilation (A) and annual catabolism (R) as A= -7.026+0.061C and R=-20.749+0.048C, respectively.

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A Study on the Equations of Estimating the Leaf Area of Broad-Leaf Species in Mt. Jiri (지리산(智異山) 주요(主要) 활엽수종(闊葉樹種)의 엽면적(葉面積) 추정식(推定式)에 대(對)한 연구(硏究))

  • Kim, Si Kyung;Lee, Kyeong Hack
    • Journal of Korean Society of Forest Science
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    • v.70 no.1
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    • pp.103-108
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    • 1985
  • This paper is concerned with estimating equations of leaf area(A) obtained from linear measurements - leaf length(L) and leaf width(W) - on the leaves of 13 species composing a natural mixed stand in Mt. Jiri. This method is known to be rapid and non-destructive in estimating leaf area. The equation of A=bLW is frequently used in rough and rapid estimation. Each species in this study has its own coefficient b according to its geometrical leaf shape. The range of coefficients of 13 species was 0.579 to 0.717. This means that the relationship A=2/3LW is suitable to most broad leaf species in a natural mixed stand in Mt. Jiri. When more precise estimation of leaf area is needed, full regression equation is used. In this study, the form of ${\log}A=b_0+b_1{\log}LW$ was the most precise estimation equation in 8 species. In addition to this, the form of $A=b_0+b_1LW$ and $A=b_0+b_1L^2+b_2W^2$ were founded to be suitable for estimation of leaf area. In comparision of these two forms, the determination coefficient were about the same, but the F-value of the former was greater than that of the latter. Therefore, the use of the former seems to be more reliable and practical.

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A Theoretical Review of Basin Storage Coefficient and Concentration Time Using the Nash Model (Nash 모형을 이용한 유역 저류상수 및 집중시간의 이론적 검토)

  • Yoo, Chul-Sang
    • Journal of Korea Water Resources Association
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    • v.42 no.3
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    • pp.235-246
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    • 2009
  • This study theoretically reviews the basin storage coefficient and concentration time using the Nash model, a simple unit hydrograph theory. First, the storage coefficient and concentration time of Nash instantaneous unit hydrograph (IUH) are derived based on their definitions, whose characteristics as well as their relationship are also reviewed. Additionally, several empirical equations of storage coefficient and concentration time commonly used in Korea are evaluated by comparing them with those for the Nash IUH. Major results of this study are summarized as follows. (1) The concentration time of Nash IUH is approximately linearly proportional to the number of linear reservoirs, but the storage coefficient non-linearly to the square root. That is, if increasing the number of linear reservoirs by four times, the concentration time becomes also increased by about four times, but the storage coefficient only about two times. This result has a special meaning to understand the effect of basin subdivision on the concentration time and storage coefficient. (2) The storage coefficient and concentration time of Nash IUH are not independent each other, so their independent estimation does not make any physical sense. As the concentration time among the two is more sensitive to the number of linear reservoirs, which should be estimated first, then the storage coefficient considering the concentration time estimated. (3) Empirical equations of concentration time can be divided into two groups, one following the linear channel theory and the other not, whose equation forms are also found to be very similar. This result indicates that the characteristic factors dominating the concentration time are very similar, indicating the possibility of its regionalization over a basin with consistent equation forms. (4) Those for storage coefficient like the Russell formulae are found to consider the physical characteristics of a basin, so their unreasonable applications could sufficiently be excluded.

Thermal Cycling Analysis of Flip-Chip BGA Solder Joints (플립 칩 BGA 솔더 접합부의 열사이클링 해석)

  • 유정희;김경섭
    • Journal of the Microelectronics and Packaging Society
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    • v.10 no.1
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    • pp.45-50
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    • 2003
  • Global full 3D finite element analysis fatigue models are constructed for flip-chip BGA on system board to predict the creep fatigue life of solder joints during the thermal cycling test. The fatigue model applied is based on Darveaux's empirical equation approach with non-linear viscoplastic analysis of solder joints. The creep life was estimated the creep life as the variations of the four kinds of thermal cycling test conditions, pad structure, composition and size of solder ball. The shortest fatigue life was obtained at the thermal cycling test condition from $-65^{\circ}C$ to $150^{\circ}C$. It was increased about 3.5 times in comparison with that from $0^{\circ}C$ to $100^{\circ}C$. At the same conditions, the fatigue life of SMD structure as the change of pad structure increased about 5.7% as compared with NSMD structure. Consequently, it was confirmed that the fatigue life became short as the creep strain energy density increased in solder joint.

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