• Title/Summary/Keyword: Least Squares Algorithm

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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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4-D Inversion of Geophysical Data Acquired over Dynamically Changing Subsurface Model (시간에 대해 변화하는 지하구조에서 획득한 물리탐사 자료의 역산)

  • Kim, Jung-Ho;Yi, Myeong-Jong
    • 한국지구물리탐사학회:학술대회논문집
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    • 2006.06a
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    • pp.117-122
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    • 2006
  • In the geophysical monitoring to understand the change of subsurface material properties with time, the time-invariant static subsurface model is commonly adopted to reconstruct a time-lapse image. This assumption of static model, however, can be invalid particularly when fluid migrates very quickly in highly permeable medium in the brine injection experiment. In such case, the resultant subsurface images may be severely distorted. In order to alleviate this problem, we develop a new least-squares inversion algorithm under the assumption that the subsurface model will change continuously in time. Instead of sampling a time-space model into numerous space models with a regular time interval, a few reference models in space domain at different times pre-selected are used to describe the subsurface structure continuously changing in time; the material property at a certain space coordinate are assumed to change linearly in time. Consequently, finding a space-time model can be simplified into obtaining several reference space models. In order to stabilize iterative inversion and to calculate meaningful subsurface images varying with time, the regularization along time axis is introduced assuming that the subsurface model will not change significantly during the data acquisition. The performance of the proposed algorithm is demonstrated by the numerical experiments using the synthetic data of crosshole dc resistivity tomography.

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An Application of loop-loop EM Method for Geotechnical Survey (지반조사를 위한 loop-loop 전자탐사 기법의 적용)

  • You Jin-Sang;Song Yoonho;Seo1 Soon-Jee;Song Young-Soo
    • Geophysics and Geophysical Exploration
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    • v.4 no.2
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    • pp.25-33
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    • 2001
  • Loop-loop electromagnetic (EM) survey in frequency domain has been carried out in order to provide basic solution to geotechnical applications. Source and receiver configuration may be horizontal co-planar (HCP) and/or vertical co-planar (VCP). Three quadrature components of mutual impedance ratio for each configuration are used to construct the subsurface image. For the purpose of obtaining the model response and validating the reasonable performance of the inversion, we obtained each responses of two-layered and three-layered earth models and two-dimensional (2-D) isolated anomalous body. The response of 2-D isolated anomalous body has been calculated using extended Born approximation for the solution of 2.5-D integral equation describing EM scattering problem. As a result of the least-squares inversion with variable Lagrangian multiplier, we could construct more resolvable image from HCP data than VCP data. Furthermore, joint inversion of HCP and VCP data made better stability and resolution of the inversion. Resistivity values, however, did not exactly match the true ones. Loop-loop EM field data was obtained with EM34-3XL system manufactured by Geonics Ltd. (Canada). Electrical resistivity survey was conducted on the same line for the comparison in advance. Since the constructed image from loop-loop EM data by 2-D inversion algorithm showed almost similar resistivity distribution to that from electrical resistivity one, we expect the developed 2.5-D loop-loop EM inversion program can be applied for the reconnaissance site survey.

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A Study of Rayleigh Damping Effect on Dynamic Crack Propagation Analysis using MLS Difference Method (MLS 차분법을 활용한 동적 균열전파해석의 Rayleigh 감쇠영향 분석)

  • Kim, Kyeong-Hwan;Lee, Sang-Ho;Yoon, Young-Cheol
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.29 no.6
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    • pp.583-590
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    • 2016
  • This paper presents a dynamic crack propagation algorithm with Rayleigh damping effect based on the MLS(Moving Least Squares) Difference Method. Dynamic equilibrium equation and constitutive equation are derived by considering Rayliegh damping and governing equations are discretized by the MLS derivative approximation; the proportional damping, which has not been properly treated in the conventional strong formulations, was implemented in both the equilibrium equation and constitutive equation. Dynamic equilibrium equation including time relevant terms is integrated by the Central Difference Method and the discrete equations are simplified by lagging the velocity one step behind. A geometrical feature of crack is modeled by imposing the traction-free condition onto the nodes placed at crack surfaces and the effect of movement and addition of the nodes at every time step due to crack growth is appropriately reflected on the construction of total system. The robustness of the proposed numerical algorithm was proved by simulating single and multiple crack growth problems and the effect of proportional damping on the dynamic crack propagation analysis was effectively demonstrated.

Three-dimensional Imaging of Subsurface Structures by Resistivity Tomography (전기비저항 토모그래피에 의한 지하구조의 3차원 영상화)

  • Yi Myeong-Jong;Kim Jung-Ho;Chung Seung-Hwan;Suh Jung Hee
    • Geophysics and Geophysical Exploration
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    • v.5 no.4
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    • pp.236-249
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    • 2002
  • We have extended the three-dimensional (3-D) resistivity imaging algorithm to cover the 3-D resistivity tomography problem, where resistivity data are acquired using electrodes installed in several boreholes as well as at the earth surface. The imaging algorithm consists of the 3-D finite element forward modeling and least-squares inversion scheme, where the ACB (Active Constraint Balancing) is adopted to enhance the resolving power of the inversion. Sensitivity analysis with numerical verifications shows that 3-D resistivity tomography is a very appealing method and can be used to get 3-D attitude of subsurface structures with very high-resolution. Moreover, we could accurately handle the topography effect, which could cause artifacts in the resistivity tomography. In the application of 3-D resistivity tomography to the real field data set acquired at the quarry mine, we could derive a very reasonable and accurate image of the subsurface.

Discrimination of African Yams Containing High Functional Compounds Using FT-IR Fingerprinting Combined by Multivariate Analysis and Quantitative Prediction of Functional Compounds by PLS Regression Modeling (FT-IR 스펙트럼 데이터의 다변량 통계분석을 이용한 고기능성 아프리칸 얌 식별 및 기능성 성분 함량 예측 모델링)

  • Song, Seung Yeob;Jie, Eun Yee;Ahn, Myung Suk;Kim, Dong Jin;Kim, In Jung;Kim, Suk Weon
    • Horticultural Science & Technology
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    • v.32 no.1
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    • pp.105-114
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    • 2014
  • We established a high throughput screening system of African yam tuber lines which contain high contents of total carotenoids, flavonoids, and phenolic compounds using ultraviolet-visible (UV-VIS) spectroscopy and Fourier transform infrared (FT-IR) spectroscopy in combination with multivariate analysis. The total carotenoids contents from 62 African yam tubers varied from 0.01 to $0.91{\mu}g{\cdot}g^{-1}$ dry weight (wt). The total flavonoids and phenolic compounds also varied from 12.9 to $229{\mu}g{\cdot}g^{-1}$ and from 0.29 to $5.2mg{\cdot}g^{-1}$dry wt. FT-IR spectra confirmed typical spectral differences between the frequency regions of 1,700-1,500, 1,500-1,300 and $1,100-950cm^{-1}$, respectively. These spectral regions were reflecting the quantitative and qualitative variations of amide I, II from amino acids and proteins ($1,700-1,500cm^{-1}$), phosphodiester groups from nucleic acid and phospholipid ($1,500-1,300cm^{-1}$) and carbohydrate compounds ($1,100-950cm^{-1}$). Principal component analysis (PCA) and subsequent partial least square-discriminant analysis (PLS-DA) were able to discriminate the 62 African yam tuber lines into three separate clusters corresponding to their taxonomic relationship. The quantitative prediction modeling of total carotenoids, flavonoids, and phenolic compounds from African yam tuber lines were established using partial least square regression algorithm from FT-IR spectra. The regression coefficients ($R^2$) between predicted values and estimated values of total carotenoids, flavonoids and phenolic compounds were 0.83, 0.86, and 0.72, respectively. These results showed that quantitative predictions of total carotenoids, flavonoids, and phenolic compounds were possible from FT-IR spectra of African yam tuber lines with higher accuracy. Therefore we suggested that quantitative prediction system established in this study could be applied as a rapid selection tool for high yielding African yam lines.

Detection of Abnormal Leakage and Its Location by Filtering of Sonic Signals at Petrochemical Plant (비정상 음향신호 필터링을 통한 플랜트 가스누출 위치 탐지기법)

  • Yoon, Young-Sam;Kim, Cheol
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.36 no.6
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    • pp.655-662
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    • 2012
  • Gas leakage in an oil refinery causes damage to the environment and unsafe conditions. Therefore, it is necessary to develop a technique that is able to detect the location of the leakage and to filter abnormal gas-leakage signals from normal background noise. In this study, the adaptation filter of the finite impulse response (FIR) least mean squares (LMS) algorithm and a cross-correlation function were used to develop a leakage-predicting program based on LABVIEW. Nitrogen gas at a high pressure of 120 kg/$cm^2$ and the assembled equipment were used to perform experiments in a reverberant chamber. Analysis of the data from the experiments performed with various hole sizes, pressures, distances, and frequencies indicated that the background noise occurred primarily at less than 1 kHz and that the leakage signal appeared in a high-frequency region of around 16 kHz. Measurement of the noise sources in an actual oil refinery revealed that the noise frequencies of pumps and compressors, which are two typical background noise sources in a petrochemical plant, were 2 kHz and 4.5 kHz, respectively. The fact that these two signals were separated clearly made it possible to distinguish leakage signals from background noises and, in addition, to detect the location of the leakage.

2D Inversion of Magnetic Data using Resolution Model Constraint (분해능 모델 제한자를 사용하는 자력탐사자료의 2차원 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.131-138
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    • 2013
  • We developed a method for inverting magnetic data to image 2D susceptibility models. The major difficulty in the inversion of the potential data is the nonuniqueness. Furthermore, generally the number of inversion blocks are greater than the number of the magnetic data available, and thus the magnetic inversion leads to under-determined problem, which aggravates the nonuniqueness. When the magnetic data were inverted by the general least-squares method, the anomalous susceptibility would be concentrated near the surface in the inverted section. To overcome this nonuniqueness problem, we propose a new resolution model constraint that is calculated from the parameter resolution. The model constraint imposes large penalty on the model parameter with good resolution, on the other hand small penalty on the model parameter with poor resolution. Thus, the deep-seated model parameter, generally having poor resolution, can be effectively resolved. The developed inversion algorithm is applied to the inversion of the synthetic data for typical models of magnetic anomalies and is tested on real airborne data obtained at the Okcheon belt of Korea.

A Study on the Numerical Modeling of the Fish Behabior to the Model Net - Parameter Estimation in Numerical Model of Fish Behavior - (모형그물에 대한 어군행동의 수직 모델링에 관한 연구 - 어군행동을 나타내는 수치 모델의 파라메터 추정 -)

  • Lee, Byoung-Gee;Lee, Dae-Jae;Chang, Ho-Young
    • Journal of the Korean Society of Fisheries and Ocean Technology
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    • v.31 no.4
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    • pp.307-325
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    • 1995
  • IN order to gain a fundamental data for forecast or control of fish behavior and evaluated the feasibility of an application of the modeling technique to a field, in this paper a numerical model for describing the behavior of fishes in a water tank was presented. The parameters of the model were estimated by using the time-series data on the three-dimensional position of fishes and by applying the least squares algorithm. The estimated parameters were standardized to examine the variation of parameters according to the number of individuals and flow speed that the mean values of parameters were to be zero and their variances were to be one. The results obtained can be summarized as follows: (1) The standardized parameter $a^*$of propulsive force decreased according to increased the number of individuals and the flow speed. (2) The standardized parameter ${k_b}^*$ of interactive force increased according to increased the number of individuals, but decreased according to the flow speed. (3) The standardized parameter ${k_c}^*$ of schooling force increased according to │increased the number of individuals and the flow speed. (4) The standardized parameter │${k_w}^{+*}$│ of repulsive force against wall or bottom increased according to increased the number of individuals, but decreased according to the flow speed. (5) The standardized parameter │${k_w}^{-*}$│ of attractive force against wall or bottom was generally constant according to increased the number of individuals, but increased according to the flow speed. (6) The standardized parameter $\upsilon$ super(*) of damping force increased according to increased the number of individuals, but decreased according to the flow speed.

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Design of Partial Discharge Pattern Classifier of Softmax Neural Networks Based on K-means Clustering : Comparative Studies and Analysis of Classifier Architecture (K-means 클러스터링 기반 소프트맥스 신경회로망 부분방전 패턴분류의 설계 : 분류기 구조의 비교연구 및 해석)

  • Jeong, Byeong-Jin;Oh, Sung-Kwun
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.67 no.1
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    • pp.114-123
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    • 2018
  • This paper concerns a design and learning method of softmax function neural networks based on K-means clustering. The partial discharge data Information is preliminarily processed through simulation using an Epoxy Mica Coupling sensor and an internal Phase Resolved Partial Discharge Analysis algorithm. The obtained information is processed according to the characteristics of the pattern using a Motor Insulation Monitoring System program. At this time, the processed data are total 4 types that void discharge, corona discharge, surface discharge and slot discharge. The partial discharge data with high dimensional input variables are secondarily processed by principal component analysis method and reduced with keeping the characteristics of pattern as low dimensional input variables. And therefore, the pattern classifier processing speed exhibits improved effects. In addition, in the process of extracting the partial discharge data through the MIMS program, the magnitude of amplitude is divided into the maximum value and the average value, and two pattern characteristics are set and compared and analyzed. In the first half of the proposed partial discharge pattern classifier, the input and hidden layers are classified by using the K-means clustering method and the output of the hidden layer is obtained. In the latter part, the cross entropy error function is used for parameter learning between the hidden layer and the output layer. The final output layer is output as a normalized probability value between 0 and 1 using the softmax function. The advantage of using the softmax function is that it allows access and application of multiple class problems and stochastic interpretation. First of all, there is an advantage that one output value affects the remaining output value and its accompanying learning is accelerated. Also, to solve the overfitting problem, L2-normalization is applied. To prove the superiority of the proposed pattern classifier, we compare and analyze the classification rate with conventional radial basis function neural networks.