• Title/Summary/Keyword: Closed form solution

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Design of a Condition-based Maintenance Policy Using a Surrogate Variable (대용변수를 이용한 상태기반 보전정책의 설계)

  • Kwon, Hyuck Moo;Hong, Sung Hoon;Lee, Min Koo
    • Journal of Korean Society for Quality Management
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    • v.49 no.3
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    • pp.299-312
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    • 2021
  • Purpose: We provide a condition-based maintenance policy where a surrogate variable is used for monitoring system performance. We constructed a risk function by taking into account the risk and losses accompanied with erroneous decisions. Methods: Assuming a unique degradation process for the performance variable and its specific relationship with the surrogate variable, the maintenance policy is determined. A risk function is developed on the basis of producer's and consumer's risks accompanied with each decision. With a strategic safety factor considered, the optimal threshold value for the surrogate variable is determined based on the risk function. Results: The condition-based maintenance is analyzed from the point of risk. With an assumed safety consideration, the optimal threshold value of the surrogate variable is provided for taking a maintenance action. The optimal solution cannot be obtained in a closed form. An illustrative numerical example and solution is provided with a source code of R program. Conclusion: The study can be applied to situation where a sensor signal is issued if the system performance begins to degrade gradually and reaches eventually its functional failure. The study can be extended to the case where two or more performance variables are connected to a same surrogate variable. Also estimation of the distribution parameters and risk coefficients should be further studied.

Predictive modeling of the compressive strength of bacteria-incorporated geopolymer concrete using a gene expression programming approach

  • Mansouri, Iman;Ostovari, Mobin;Awoyera, Paul O.;Hu, Jong Wan
    • Computers and Concrete
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    • v.27 no.4
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    • pp.319-332
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    • 2021
  • The performance of gene expression programming (GEP) in predicting the compressive strength of bacteria-incorporated geopolymer concrete (GPC) was examined in this study. Ground-granulated blast-furnace slag (GGBS), new bacterial strains, fly ash (FA), silica fume (SF), metakaolin (MK), and manufactured sand were used as ingredients in the concrete mixture. For the geopolymer preparation, an 8 M sodium hydroxide (NaOH) solution was used, and the ambient curing temperature (28℃) was maintained for all mixtures. The ratio of sodium silicate (Na2SiO3) to NaOH was 2.33, and the ratio of alkaline liquid to binder was 0.35. Based on experimental data collected from the literature, an evolutionary-based algorithm (GEP) was proposed to develop new predictive models for estimating the compressive strength of GPC containing bacteria. Data were classified into training and testing sets to obtain a closed-form solution using GEP. Independent variables for the model were the constituent materials of GPC, such as FA, MK, SF, and Bacillus bacteria. A total of six GEP formulations were developed for predicting the compressive strength of bacteria-incorporated GPC obtained at 1, 3, 7, 28, 56, and 90 days of curing. 80% and 20% of the data were used for training and testing the models, respectively. R2 values in the range of 0.9747 and 0.9950 (including train and test dataset) were obtained for the concrete samples, which showed that GEP can be used to predict the compressive strength of GPC containing bacteria with minimal error. Moreover, the GEP models were in good agreement with the experimental datasets and were robust and reliable. The models developed could serve as a tool for concrete constructors using geopolymers within the framework of this research.

A Study on the International R&D Competition and Optimal Tariff (국제 R&D 경쟁과 최적관세)

  • Li, Dong-Sheng;Lee, Jong-Min
    • Korea Trade Review
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    • v.41 no.2
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    • pp.29-60
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    • 2016
  • Research and Development(R&D) investment is an issue of central importance in any economy. In this paper we analyze the relationship between R&D spillovers and trade-related variables, using a two-stage model where duopolists simultaneously decide on R&D in the first stage and engage in Cournot competition in the second stage. We characterized and compared the free-trade and trade-restriction R&D equilibrium in a two-stage game of R&D investment followed by Cournot market competition. We also assessed the impact of varying the R&D spillover on the equilibrium outcomes and tariff. We showed for both free trade and protection cases that there exists a unique symmetric solution(subgame perfect Nash equilibrium). As the solution, while analytical, cannot be stated in closed form, we resorted to numerical experiments to investigate the equilibrium results. Our estimates indicate for both free trade and protection cases that the level of R&D investment and the rate of R&D expenditure decrease as the degree of R&D spillovers increases, and that there is an inverse relation between the degree of R&D spillovers and level of protection. The latter implies that the larger the degree of R&D spillovers, the lesser the level of protection.

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TiO2 Nanotubular Formation on Grade II Pure Titanium by Short Anodization Processing (Grade II 순수 타이타늄의 단시간 양극산화에 의한 TiO2 나노튜브 형성)

  • Lee, Kwangmin;Kim, Yongjae;Kang, Kyungho;Yoon, Duhyeon;Rho, Sanghyun;Kang, Seokil;Yoo, Daeheung;Lim, Hyunpil;Yun, Kwiduk;Park, Sangwon;Kim, Hyun Seung
    • Korean Journal of Materials Research
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    • v.23 no.4
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    • pp.240-245
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    • 2013
  • Electrochemical surface treatment is commonly used to form a thin, rough, and porous oxidation layer on the surface of titanium. The purpose of this study was to investigate the formation of nanotubular titanium oxide arrays during short anodization processing. The specimen used in this study was 99.9% pure cp-Ti (ASTM Grade II) in the form of a disc with diameter of 15 mm and a thickness of 1 mm. A DC power supplier was used with the anodizing apparatus, and the titanium specimen and the platinum plate ($3mm{\times}4mm{\times}0.1mm$) were connected to an anode and cathode, respectively. The progressive formation of $TiO_2$ nanotubes was observed with FE-SEM (Field Emission Scanning Electron Microscopy). Highly ordered $TiO_2$ nanotubes were formed at a potential of 20 V in a solution of 1M $H_3PO_4$ + 1.5 wt.% HF for 10 minutes, corresponding with steady state processing. The diameters and the closed ends of $TiO_2$ nanotubes measured at a value of 50 cumulative percent were 100 nm and 120 nm, respectively. The $TiO_2$ nanotubes had lengths of 500 nm. As the anodization processing reached 10 minutes, the frequency distribution for the diameters and the closed ends of the $TiO_2$ nanotubes was gradually reduced. Short anodization processing for $TiO_2$ nanotubes of within 10 minutes was established.

On the Performance Analysis of Blind Equalization for Parial Response Channels (부분응답 채널에 대한 블라인드 등화기의 성능분석)

  • Lee, Sang-Kyung;Lee, Jae-Chon
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.28 no.4C
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    • pp.413-423
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    • 2003
  • The CMA algorithmis most widely investigated blind algorithm and the most widely used one in practice. But, since nonlinear CM cost function have not closed form solution about the optimum weight. There have been difficultiesto analyze the CMA equalizer's theoretical performance. Recently, Zeng presents the notable theoretical resultabout the MSE of CM-minimizing estimators for the FIR linear channel in the presence of AWGN. Through this method, It wouldbe possible to campare the theoretical performance between CMA and Wiener equalizer in terms of MSE. In this paper, based on Zeng's method, we first calculate the theoretical MSE bound of CMA equalizer in partial response channel which is widely used in HDD, digital VCR such as high-density digital recording.playback systems. We confirmedthis result withthe computer simulation. Except this, we also performedthe theoretical and simulation analysis about the modified CMA equalizer, which was proposed to improve the performance of CMA equalizer in partial response channel. Finally, we compare and evaluate the performance analysis results between CMA and Modified CMA equalizer.

Stereo Vision based on Planar Algebraic Curves (평면대수곡선을 기반으로 한 스테레오 비젼)

  • Ahn, Min-Ho;Lee, Chung-Nim
    • Journal of KIISE:Software and Applications
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    • v.27 no.1
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    • pp.50-61
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    • 2000
  • Recently the stereo vision based on conics has received much attention by many authors. Conics have many features such as their matrix expression, efficient correspondence checking, abundance of conical shapes in real world. Extensions to higher algebraic curves met with limited success. Although irreducible algebraic curves are rather rare in the real world, lines and conics are abundant whose products provide good examples of higher algebraic curves. We consider plane algebraic curves of an arbitrary degree $n{\geq}2$ with a fully calibrated stereo system. We present closed form solutions to both correspondence and reconstruction problems. Let $f_1,\;f_2,\;{\pi}$ be image curves and plane and $VC_P(g)$ the cone with generator (plane) curve g and vertex P. Then the relation $VC_{O1}(f_1)\;=\;VC_{O1}(VC_{O2}(f_2)\;∩\;{\pi})$ gives polynomial equations in the coefficient $d_1,\;d_2,\;d_3$ of the plane ${\pi}$. After some manipulations, we get an extremely simple polynomial equation in a single variable whose unique real positive root plays the key role. It is then followed by evaluating $O(n^2)$ polynomials of a single variable at the root. It is in contrast to the past works which usually involve a simultaneous system of multivariate polynomial equations. We checked our algorithm using synthetic as well as real world images.

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브란운관의 후면유리 폐기물을 이용한 제올라이트 합성

  • Jang, Yeong-Nam;Bae, In-Guk;Chae, Su-Cheon;Ryu, Gyeong-Won
    • Journal of the Korean Professional Engineers Association
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    • v.34 no.2
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    • pp.167-173
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    • 2001
  • Through alkaline hydrothermal activation processes, Na-A type zeolite was synthesized as a single phase withfunnel-glass waste from a television tube factory. The autoclaving was performed in a closed teflon vessel in therange of 80~95"C. The silica-rich solution as a starting material was hydrothermally synthesized with quartz in INNaOH by heating 350"C under the pressure of 1,500 atm. NaA102 was made from NaOH and Al(OH)3 by heating95"c for 2~3 hours and the molar ratios of it were Na20/A1203=1.4 and H20Ha20=8. The equi-dimensional Atype zeolite (1 ~2 U) was formed by the simple mixing of'the silica-rich solution, glass waste and NaA102 for I~3hours-heating at 80"C. The characterization of the reaction product shows Na-A as a single phase. The synthesizedzeolite has cube-dodecahedral form and Ca2+ ion exchange capacity of the Na-A was in the range of 215~220mequivalent/100 g.20mequivalent/100 g.

Synthesis of Na-A Type of Zeolite from Funnel-Glass Waste (브라운관의 후면유리 폐기물을 이용한 제올라이트 합성)

  • 장영남;배인국;채수천;류경원
    • Economic and Environmental Geology
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    • v.34 no.2
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    • pp.167-173
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    • 2001
  • Through alkaline hydrothermal activation processes, Na-A type zeolite was synthesized as a single phase with funnel-glass waste from a television tube factory. The autoclaving was performed in a closed teflon vessel in the range of 80~95$^{\circ}$C. The silica-rich solution as a starting material was hydrothermally synthesized with quartz in IN NaOH by heating 350uC under the pressure of 1,500 atm. $NaAlO_2$ was made from NaOH and Al(OHh by heating 95$^{\circ}$C for 2-3 hours and the molar ratios of it were $Na_2O/Al_2O_3$ = 1.4 and $H_2O/Na_2O$=8. The equi-dimensional A type zeolite (1-2 11) was formed by the simple mixing of the silica-rich solution, glass waste and $NaAlO_23$ for 1-3 hours-heating at $80^{\circ}C$. The characterization of the reaction product shows Na-A as a single phase. The synthesized zeolite has cuba-dodecahedral form and $Ca^{2+}$ ion exchange capacity of the Na-A was in the range of 215-220 mequiva1entilOO g.

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A Permeable Wedge Crack in a Piezoelectric Material Under Antiplane Deformation (면외변형하의 압전재료에 대한 침투 쐐기균열)

  • Choi, Sung Ryul;Park, Jai Hak
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.39 no.9
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    • pp.859-869
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    • 2015
  • In this study, we analyze the problem of wedge cracks, which are geometrically unsymmetrical in transversely piezoelectric materials. A single concentrated antiplane mechanical load and inplane electrical load are applied at the point of the wedge surface, while one concentrated antiplane load is applied at the crack surface. The crack surfaces are considered as permeable thin slits, where both the normal component of electric displacement and the electric potential are assumed to be continuous across these slits. Using Mellin transform method, the problem is formulated and the Wiener-Hopf equation is derived. By solving the equation, the solution is obtained in a closed form. The intensity factors of the stress and the electric displacement are obtained for any crack length as well as inclined and wedge angles. Based on the results, the intensity factors are independent of the applied electric loads. The electric displacement intensity factor is always dependent on that of stress intensity factor, while the electric field intensity factor is zero. In addition, the energy release rate is computed. These solutions can be used as fundamental solutions which can be superposed to arbitrary electromechanical loadings.

Buckling analysis of elastically-restrained steel plates under eccentric compression

  • Qin, Ying;Shu, Gan-Ping;Du, Er-Feng;Lu, Rui-Hua
    • Steel and Composite Structures
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    • v.29 no.3
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    • pp.379-389
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    • 2018
  • In this research, the explicit closed-form local buckling solution of steel plates in contact with concrete, with both loaded and unloaded edges elastically restrained against rotation and subjected to eccentric compression is presented. The Rayleigh-Rize approach is applied to establish the eigenvalue problem for the local buckling performance. Buckling shape which combines trigonometric and biquadratic functions is introduced according to that used by Qin et al. (2017) on steel plate buckling under uniform compression. Explicit solutions for predicting the local buckling stress of steel plate are obtained in terms of the rotational stiffness. Based on different boundary conditions, simply yet explicit local buckling solutions are discussed in details. The proposed formulas are validated against previous research and finite element results. The influences of the loading stress gradient parameter, the aspect ratio, and the rotational stiffness on the local buckling stress resultants of steel plates with different boundary conditions were evaluated. This work can be considered as an alternative to apply a different buckling shape function to study the buckling problem of steel plate under eccentric compression comparing to the work by Qin et al. (2018), and the results are found to be in consistent with those in Qin et al. (2018).