• Title/Summary/Keyword: Weighted Mean Squared Error

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Recursive Least Squares Run-to-Run Control with Time-Varying Metrology Delays

  • Fan, Shu-Kai;Chang, Yuan-Jung
    • Industrial Engineering and Management Systems
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    • v.9 no.3
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    • pp.262-274
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    • 2010
  • This article investigates how to adaptively predict the time-varying metrology delay that could realistically occur in the semiconductor manufacturing practice. Metrology delays pose a great challenge for the existing run-to-run (R2R) controllers, driving the process output significantly away from target if not adequately predicted. First, the expected asymptotic double exponentially weighted moving average (DEWMA) control output, by using the EWMA and recursive least squares (RLS) prediction methods, is derived. It has been found that the relationships between the expected control output and target in both estimation methods are parallel, and six cases are addressed. Within the context of time-varying metrology delay, this paper presents a modified recursive least squares-linear trend (RLS-LT) controller, in combination with runs test. Simulated single input-single output (SISO) R2R processes subject to various time-varying metrology delay scenarios are used as a testbed to evaluate the proposed algorithms. The simulation results indicate that the modified RLS-LT controller can yield the process output more accurately on target with smaller mean squared error (MSE) than the original RLSLT controller that only deals with constant metrology delays.

A Study on Delivery Accuracy Using the Correlation between Errors (오차간의 상관관계를 이용하는 체계명중률 예측에 관한 연구)

  • Kim, Hyun Soo;Kim, Gunin;Kang, Hwan Il
    • The Journal of the Convergence on Culture Technology
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    • v.4 no.3
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    • pp.299-303
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    • 2018
  • Generally, when predicting the accuracy of the anti-air artillery system, the error is classified as fixed bias, variable bias, and random error. Then the standard deviation on the target is expressed as the square root of the squared sum of each error value which comes from the random error and variable bias and in the case of fixed bias, the mean value is shifted as the sum of errors from the fixed bias. At this time, the variables indicating the displacement of the direction of azimuth and elevation direction with regard to the change of the unit value of each error are weighted. These errors are then used to predict the system's delivery accuracy through a normally distributed integral. This paper presents a method of predicting system accuracy by considering the correlation of errors. This approach shows that it helps to predict the delivery accuracy of the system, precisely.

Design of Optimal FIR Filters for Data Transmission (데이터 전송을 위한 최적 FIR 필터 설계)

  • 이상욱;이용환
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.18 no.8
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    • pp.1226-1237
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    • 1993
  • For data transmission over strictly band-limited non-ideal channels, different types of filters with arbitrary responses are needed. In this paper. we proposed two efficient techniques for the design of such FIR filters whose response is specified in either the time or the frequency domain. In particular when a fractionally-spaced structure is used for the transceiver, these filters can be efficiently designed by making use of characteristics of oversampling. By using a minimum mean-squared error criterion, we design a fractionally-spaced FIR filter whose frequency response can be controlled without affecting the output error. With proper specification of the shape of the additive noise signals, for example, the design results in a receiver filter that can perform compromise equalization as well as phase splitting filtering for QAM demodulation. The second method ad-dresses the design of an FIR filter whose desired response can be arbitrarily specified in the frequency domain. For optimum design, we use an iterative optimization technique based on a weighted least mean square algorithm. A new adaptation algorithm for updating the weighting function is proposed for fast and stable convergence. It is shown that these two independent methods can be efficiently combined together for more complex applications.

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Prediction Acidity Constant of Various Benzoic Acids and Phenols in Water Using Linear and Nonlinear QSPR Models

  • Habibi Yangjeh, Aziz;Danandeh Jenagharad, Mohammad;Nooshyar, Mahdi
    • Bulletin of the Korean Chemical Society
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    • v.26 no.12
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    • pp.2007-2016
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    • 2005
  • An artificial neural network (ANN) is successfully presented for prediction acidity constant (pKa) of various benzoic acids and phenols with diverse chemical structures using a nonlinear quantitative structure-property relationship. A three-layered feed forward ANN with back-propagation of error was generated using six molecular descriptors appearing in the multi-parameter linear regression (MLR) model. The polarizability term $(\pi_1)$, most positive charge of acidic hydrogen atom $(q^+)$, molecular weight (MW), most negative charge of the acidic oxygen atom $(q^-)$, the hydrogen-bond accepting ability $(\epsilon_B)$ and partial charge weighted topological electronic (PCWTE) descriptors are inputs and its output is pKa. It was found that properly selected and trained neural network with 205 compounds could fairly represent dependence of the acidity constant on molecular descriptors. For evaluation of the predictive power of the generated ANN, an optimized network was applied for prediction pKa values of 37 compounds in the prediction set, which were not used in the optimization procedure. Squared correlation coefficient $(R^2)$ and root mean square error (RMSE) of 0.9147 and 0.9388 for prediction set by the MLR model should be compared with the values of 0.9939 and 0.2575 by the ANN model. These improvements are due to the fact that acidity constant of benzoic acids and phenols in water shows nonlinear correlations with the molecular descriptors.

A Demand Forecasting for Aircraft Spare Parts using ARMIA (ARIMA를 이용한 항공기 수리부속의 수요 예측)

  • Park, Young-Jin;Jeon, Geon-Wook
    • Journal of the military operations research society of Korea
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    • v.34 no.2
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    • pp.79-101
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    • 2008
  • This study is for improvement of repair part demand forecasting method of Republic of Korea Air Force aircraft. Recently, demand prediction methods are Weighted moving average, Linear moving average, Trend analysis, Simple exponential smoothing, Linear exponential smoothing. But these use fixed weight and moving average range. Also, NORS(Not Operationally Ready upply) is increasing. Recommended method of Box-Jenkins' ARIMA can solve problems of these method and improve estimate accuracy. To compare recent prediction method and ARIMA that use mean squared error(MSE) is reacted sensitively in change of error. ARIMA has high accuracy than existing forecasting method. If apply this method of study in other several Items, can prove demand forecast Capability.

Design of Modeling & Simulator for ASP Realized with the Aid of Polynomiai Radial Basis Function Neural Networks (다항식 방사형기저함수 신경회로망을 이용한 ASP 모델링 및 시뮬레이터 설계)

  • Kim, Hyun-Ki;Lee, Seung-Joo;Oh, Sung-Kwun
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.62 no.4
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    • pp.554-561
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    • 2013
  • In this paper, we introduce a modeling and a process simulator developed with the aid of pRBFNNs for activated sludge process in the sewage treatment system. Activated sludge process(ASP) of sewage treatment system facilities is a process that handles biological treatment reaction and is a very complex system with non-linear characteristics. In this paper, we carry out modeling by using essential ASP factors such as water effluent quality, the manipulated value of various pumps, and water inflow quality, and so on. Intelligent algorithms used for constructing process simulator are developed by considering multi-output polynomial radial basis function Neural Networks(pRBFNNs) as well as Fuzzy C-Means clustering and Particle Swarm Optimization. Here, the apexes of the antecedent gaussian functions of fuzzy rules are decided by C-means clustering algorithm and the apexes of the consequent part of fuzzy rules are learned by using back-propagation based on gradient decent method. Also, the parameters related to the fuzzy model are optimized by means of particle swarm optimization. The coefficients of the consequent polynomial of fuzzy rules and performance index are considered by the Least Square Estimation and Mean Squared Error. The descriptions of developed process simulator architecture and ensuing operation method are handled.

Design-Based Properties of Least Square Estimators of Panel Regression Coefficients Based on Complex Panel Data (복합패널 데이터에 기초한 최소제곱 패널회귀추정량의 설계기반 성질)

  • Kim, Kyu-Seong
    • Communications for Statistical Applications and Methods
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    • v.17 no.4
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    • pp.515-525
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    • 2010
  • We investigated design-based properties of the ordinary least square estimator(OLSE) and the weighted least square estimator(WLSE) in a panel regression model. Given a complex data we derive the magnitude of the design-based bias of two estimators and show that the bias of WLSE is smaller than that of OLSE. We also conducted a simulation study using Korean welfare panel data in order to compare design-based properties of two estimators numerically. In the study we found the followings. First, the relative bias of OLSE is nearly two times larger than that of WLSE and the bias ratio of OLSE is greater than that of WLSE. Also the relative bias of OLSE remains steady but that of WLSE becomes smaller as the sample size increases. Next, both the variance and mean square error(MSE) of two estimators decrease when the sample size increases. Also there is a tendency that the proportion of squared bias in MSE of OLSE increases as the sample size increase, but that of WLSE decreases. Finally, the variance of OLSE is smaller than that of WLSE in almost all cases and the MSE of OLSE is smaller in many cases. However, the number of cases of larger MSE of OLSE increases when the sample size increases.

Zircon U-Pb and Rare Earth Elements Analyses on Banded Gneiss in Euiam Gneiss Complex, Central Gyeonggi Massif: Consideration for the Timing of Depositional Event and Metamorphism of the Basement Rocks in the Gyeonggi Massif (경기육괴 중부 의암 편마암 복합체 호상편마암의 저어콘 U-Pb 연령과 미량원소: 경기육괴 기반암의 퇴적 시기와 변성작용에 대한 고찰)

  • Lee, Byung Choon;Cho, Deung-Lyong
    • Korean Journal of Mineralogy and Petrology
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    • v.35 no.3
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    • pp.215-233
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    • 2022
  • The zircon U-Pb and trace element analyses were performed for banded gneiss in the Euiam gneiss complex, central Gyeonggi Massif. An age of detrital zircon shows predominant age peaks at ca. 2500-2480 Ma with numerous ages ranging from Siderian to Rhyacian period. The youngest age peak of detrital zircon constrains the maximum deposition age of protolith of banded gneiss at ca. 2070 Ma. Meanwhile, the zircon rim yielded metamorphic age of ca. 1966 ± 39 Ma ~ 1918 ± 13 Ma. Based on the error range, degree of discordancy, and value of mean squared weighted deviation, we considered that the age of 1918 ± 13 Ma is the most reasonable age indicating the timing of metamorphism for banded gneiss. The zircon rims yield Ti-in-zircon crystallization temperature of 690-740℃. Therefore, we suggested that there was a high-grade metamorphic event in the Gyeonggi Massif at ca. 1918 Ma which is older than the metamorphic event that occurred in the Gyeonggi Massif during ca. 1880-1860 Ma.