• Title/Summary/Keyword: Sum of squares

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Weighted Least Absolute Deviation Lasso Estimator

  • Jung, Kang-Mo
    • Communications for Statistical Applications and Methods
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    • v.18 no.6
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    • pp.733-739
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    • 2011
  • The linear absolute shrinkage and selection operator(Lasso) method improves the low prediction accuracy and poor interpretation of the ordinary least squares(OLS) estimate through the use of $L_1$ regularization on the regression coefficients. However, the Lasso is not robust to outliers, because the Lasso method minimizes the sum of squared residual errors. Even though the least absolute deviation(LAD) estimator is an alternative to the OLS estimate, it is sensitive to leverage points. We propose a robust Lasso estimator that is not sensitive to outliers, heavy-tailed errors or leverage points.

Modeling and Parametric Studies on Moment-Curvature Relation of a Reinforced Concrete Column Subject In Axial-toad and Bi-Axil Moment (축하중과 이축모멘트를 받는 철근콘크리트 기둥의 모멘트-곡률에 관한 모델링 및 변수고찰)

  • 이차돈;최기봉;차준실;김성진
    • Journal of the Korea Concrete Institute
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    • v.14 no.5
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    • pp.677-688
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    • 2002
  • A analytical model is developed which can simulate a complete inelastic biaxial moment-curvature relations of a reinforced concrete column. The model can simulate sudden drop in moment capacity after peak moment and due to spalling of cover concrete. Parametric studies are performed examine the effects of constituent material properties as well as topological arrangement of reinforcements on moment-curvature relations and P-M interaction curve. It has been analytically observed that ductility of a reinforced concrete column is influenced mostly by magnitude of the axial load and spacings or the volume of lateral reinforcements. Compared to ACI P-M interaction curve, overall increase about 10% in square root of sum of squares of axial force and moment, and about 20% in peak load are observed for the columns reinforced according to ACI seismic design code.

The NHPP Bayesian Software Reliability Model Using Latent Variables (잠재변수를 이용한 NHPP 베이지안 소프트웨어 신뢰성 모형에 관한 연구)

  • Kim, Hee-Cheul;Shin, Hyun-Cheul
    • Convergence Security Journal
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    • v.6 no.3
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    • pp.117-126
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    • 2006
  • Bayesian inference and model selection method for software reliability growth models are studied. Software reliability growth models are used in testing stages of software development to model the error content and time intervals between software failures. In this paper, could avoid multiple integration using Gibbs sampling, which is a kind of Markov Chain Monte Carlo method to compute the posterior distribution. Bayesian inference for general order statistics models in software reliability with diffuse prior information and model selection method are studied. For model determination and selection, explored goodness of fit (the error sum of squares), trend tests. The methodology developed in this paper is exemplified with a software reliability random data set introduced by of Weibull distribution(shape 2 & scale 5) of Minitab (version 14) statistical package.

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Estimable functions of mixed models (혼합모형의 추정가능함수)

  • Choi, Jaesung
    • The Korean Journal of Applied Statistics
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    • v.29 no.2
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    • pp.291-299
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    • 2016
  • This paper discusses how to establish estimable functions when there are fixed and random effects in design models. It proves that estimable functions of mixed models are not related to random effects. A fitting constants method is used to obtain sums of squares due to random effects and Hartley's synthesis is used to calculate coefficients of variance components. To test about the fixed effects the degrees of freedom associated with divisor are determined by means of the Satterthwaite approximation.

Estimation for random coefficient autoregressive model (확률계수 자기회귀 모형의 추정)

  • Kim, Ju Sung;Lee, Sung Duck;Jo, Na Rae;Ham, In Suk
    • The Korean Journal of Applied Statistics
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    • v.29 no.1
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    • pp.257-266
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    • 2016
  • Random Coefficient Autoregressive models (RCA) have attracted increased interest due to the wide range of applications in biology, economics, meteorology and finance. We consider an RCA as an appropriate model for non-linear properties and better than an AR model for linear properties. We study the methods of RCA parameter estimation. Especially we proposed the special case that an random coefficient ${\phi}(t)$ has the initial value ${\phi}(0)$ in the RCA model. In practical study, we estimated the parameters and compared Prediction Error Sum of Squares (PRESS) criterion between AR and RCA using Korean Mumps data.

Securing a Cyber Physical System in Nuclear Power Plants Using Least Square Approximation and Computational Geometric Approach

  • Gawand, Hemangi Laxman;Bhattacharjee, A.K.;Roy, Kallol
    • Nuclear Engineering and Technology
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    • v.49 no.3
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    • pp.484-494
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    • 2017
  • In industrial plants such as nuclear power plants, system operations are performed by embedded controllers orchestrated by Supervisory Control and Data Acquisition (SCADA) software. A targeted attack (also termed a control aware attack) on the controller/SCADA software can lead a control system to operate in an unsafe mode or sometimes to complete shutdown of the plant. Such malware attacks can result in tremendous cost to the organization for recovery, cleanup, and maintenance activity. SCADA systems in operational mode generate huge log files. These files are useful in analysis of the plant behavior and diagnostics during an ongoing attack. However, they are bulky and difficult for manual inspection. Data mining techniques such as least squares approximation and computational methods can be used in the analysis of logs and to take proactive actions when required. This paper explores methodologies and algorithms so as to develop an effective monitoring scheme against control aware cyber attacks. It also explains soft computation techniques such as the computational geometric method and least squares approximation that can be effective in monitor design. This paper provides insights into diagnostic monitoring of its effectiveness by attack simulations on a four-tank model and using computation techniques to diagnose it. Cyber security of instrumentation and control systems used in nuclear power plants is of paramount importance and hence could be a possible target of such applications.

Vibration Prediction and Charge Estimation in Hard Rock Blasting Site (경암층 발파현장에서 진동예측 및 장약량산정)

  • Park, Yeon-Soo;Park, Sun-Joon;Choi, Sun-Min;Mun, Soo-Bong;Mun, Byeong-Ok;Jeong, Gyung-Yul;Jeong, Tae-Hyeong;Hwang, Seung-Ill;Kim, Min-Jung;Park, Sang-Chul;Kim, Jung-Ju;Lee, Byeong-Geun
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.19 no.3
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    • pp.313-319
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    • 2009
  • The blasting has a lot of economic efficiency and speediness but it can damage to a neighbor structure, a domestic animal and a cultured fish due to the blasting vibration, then the public grievance is increased. Therefore, we need to manage the blasting vibration efficiently. The prediction of the correct vibration velocity is not easy because there are lots of different kinds of the scale of blasting vibration and it has a number of a variable effect. So we figure the optimum line through the least-squares regression by using the vibration data measured in hard rock blasting and compared with the design vibration prediction equation. As a result, we confirm that the vibration estimated in this paper is bigger than the design vibration prediction equation in the same charge and distance. If there is a Gaussian normal distribution data on the left-right side of the least squares regression, then we can estimate the vibration prediction equation on reliability 50%(${\beta}=0$), 90%(${\beta}=1.28$), 95%(${\beta}=1.64$). 99.9%(${\beta}=3.09$). As a result, it appears to be suitable that the reliability is 99% at the transverse component, the reliability 95% is at the vertical component, the reliability 90% is at the longitudinal component and the reliability is 95% at the peak vector sum component.

THE ZAGREB INDICES OF BIPARTITE GRAPHS WITH MORE EDGES

  • XU, KEXIANG;TANG, KECHAO;LIU, HONGSHUANG;WANG, JINLAN
    • Journal of applied mathematics & informatics
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    • v.33 no.3_4
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    • pp.365-377
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    • 2015
  • For a (molecular) graph, the first and second Zagreb indices (M1 and M2) are two well-known topological indices, first introduced in 1972 by Gutman and Trinajstić. The first Zagreb index M1 is equal to the sum of the squares of the degrees of the vertices, and the second Zagreb index M2 is equal to the sum of the products of the degrees of pairs of adjacent vertices. Let $K_{n_1,n_2}^{P}$ with n1 $\leq$ n2, n1 + n2 = n and p < n1 be the set of bipartite graphs obtained by deleting p edges from complete bipartite graph Kn1,n2. In this paper, we determine sharp upper and lower bounds on Zagreb indices of graphs from $K_{n_1,n_2}^{P}$ and characterize the corresponding extremal graphs at which the upper and lower bounds on Zagreb indices are attained. As a corollary, we determine the extremal graph from $K_{n_1,n_2}^{P}$ with respect to Zagreb coindices. Moreover a problem has been proposed on the first and second Zagreb indices.

Automatic Selection of Optimal Parameter for Baseline Correction using Asymmetrically Reweighted Penalized Least Squares (Asymmetrically Reweighted Penalized Least Squares을 이용한 기준선 보정에서 최적 매개변수 자동 선택 방법)

  • Park, Aaron;Baek, Sung-June;Park, Jun-Qyu;Seo, Yu-Gyung;Won, Yonggwan
    • Journal of the Institute of Electronics and Information Engineers
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    • v.53 no.3
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    • pp.124-131
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    • 2016
  • Baseline correction is very important due to influence on performance of spectral analysis in application of spectroscopy. Baseline is often estimated by parameter selection using visual inspection on analyte spectrum. It is a highly subjective procedure and can be tedious work especially with a large number of data. For these reasons, it is an objective and automatic procedure is necessary to select optimal parameter value for baseline correction. Asymmetrically reweighted penalized least squares (arPLS) based on penalized least squares was proposed for baseline correction in our previous study. The method uses a new weighting scheme based on the generalized logistic function. In this study, we present an automatic selection of optimal parameter for baseline correction using arPLS. The method computes fitness and smoothness values of fitted baseline within available range of parameters and then selects optimal parameter when the sum of normalized fitness and smoothness gets minimum. According to the experimental results using simulated data with varying baselines, sloping, curved and doubly curved baseline, and real Raman spectra, we confirmed that the proposed method can be effectively applied to optimal parameter selection for baseline correction using arPLS.

Voltage Stability Enhancement by Optimal Placement of UPFC

  • Kowsalya, M.;Ray, K.K.;Shipurkar, Udai;Saranathan
    • Journal of Electrical Engineering and Technology
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    • v.4 no.3
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    • pp.310-314
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    • 2009
  • This paper presents the improvement of the voltage profiles of power system networks by the inclusion of Unified Power Flow Controller (UPFC). The mathematical model of the UPFC is incorporated in the load flow algorithm and the L-index is calculated for the different values of the control parameter r $and{\gamma}$. The positioning of the UPFC device is changed to minimize the sum of the squares of the L-indices at all load buses. The test cases considered for the improvement of voltage profile with the WSCC 9-bus and IEEE 30 bus system. With the best position of UPFC along with the control parameters the improvement in voltage profile of the power system networks are obtained. The results obtained are quite encouraging compared with other techniques used to identify the best location of UPFC.