• Title/Summary/Keyword: quadratic term

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Performance of Cu-SiO2 Aerogel Catalyst in Methanol Steam Reforming: Modeling of hydrogen production using Response Surface Methodology and Artificial Neuron Networks

  • Taher Yousefi Amiri;Mahdi Maleki-Kakelar;Abbas Aghaeinejad-Meybodi
    • Korean Chemical Engineering Research
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    • 제61권2호
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    • pp.328-339
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    • 2023
  • Methanol steam reforming (MSR) is a promising method for hydrogen supplying as a critical step in hydrogen fuel cell commercialization in mobile applications. Modelling and understanding of the reactor behavior is an attractive research field to develop an efficient reformer. Three-layer feed-forward artificial neural network (ANN) and Box-Behnken design (BBD) were used to modelling of MSR process using the Cu-SiO2 aerogel catalyst. Furthermore, impacts of the basic operational variables and their mutual interactions were studied. The results showed that the most affecting parameters were the reaction temperature (56%) and its quadratic term (20.5%). In addition, it was also found that the interaction between temperature and Steam/Methanol ratio is important on the MSR performance. These models precisely predict MSR performance and have great agreement with experimental results. However, on the basis of statistical criteria the ANN technique showed the greater modelling ability as compared with statistical BBD approach.

Number Field Sieve에서의 두 삼차 다항식 선택 (Two Cubic Polynomials Selection for the Number Field Sieve)

  • 조국화;구남훈;권순학
    • 한국통신학회논문지
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    • 제36권10C호
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    • pp.614-620
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    • 2011
  • 현재 가장 많이 쓰이는 공개키 암호시스템 중 하나인 RSA는 매우 큰 합성수 N의 인수분해가 어렵다는 것에 기반을 두고 있다. 120자리보다 큰 합성수를 인수분해하는데 가장 효율적인 알고리즘으로 알려진 Number Field Sieve (NFS)는 법 N에 대하여 공통근을 갖는 두 다항식 선택한 후에, sieving, linear algebra, square root 단계를 차례대로 거친다. 최근의 많은 연구 결과에 따르면 다항식을 얼마나 적합하게 선택하느냐에 따라 sieving step에서의 복잡도가 크게 달라질 수 있다는 것이 알려져 있다. Sieving 다항식은 차수가 같은 두 다항식을 선택하는 것이 이상적이며 두 개의 2차 다항식을 선택하는 방법은 이미 Montgomery가 제시하였다. 이 논문에서는 5항 등 비수열 방법을 이용하여 두 개의 3차 다항식 선택방법을 제시하고자 한다.

SHM-based probabilistic representation of wind properties: statistical analysis and bivariate modeling

  • Ye, X.W.;Yuan, L.;Xi, P.S.;Liu, H.
    • Smart Structures and Systems
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    • 제21권5호
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    • pp.591-600
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    • 2018
  • The probabilistic characterization of wind field characteristics is a significant task for fatigue reliability assessment of long-span railway bridges in wind-prone regions. In consideration of the effect of wind direction, the stochastic properties of wind field should be represented by a bivariate statistical model of wind speed and direction. This paper presents the construction of the bivariate model of wind speed and direction at the site of a railway arch bridge by use of the long-term structural health monitoring (SHM) data. The wind characteristics are derived by analyzing the real-time wind monitoring data, such as the mean wind speed and direction, turbulence intensity, turbulence integral scale, and power spectral density. A sequential quadratic programming (SQP) algorithm-based finite mixture modeling method is proposed to formulate the joint distribution model of wind speed and direction. For the probability density function (PDF) of wind speed, a double-parameter Weibull distribution function is utilized, and a von Mises distribution function is applied to represent the PDF of wind direction. The SQP algorithm with multi-start points is used to estimate the parameters in the bivariate model, namely Weibull-von Mises mixture model. One-year wind monitoring data are selected to validate the effectiveness of the proposed modeling method. The optimal model is jointly evaluated by the Bayesian information criterion (BIC) and coefficient of determination, $R^2$. The obtained results indicate that the proposed SQP algorithm-based finite mixture modeling method can effectively establish the bivariate model of wind speed and direction. The established bivariate model of wind speed and direction will facilitate the wind-induced fatigue reliability assessment of long-span bridges.

로지스틱회귀모형의 변수선택에서 로그-오즈 그래프를 통한 로그-밀도비 연구 (A study on log-density with log-odds graph for variable selection in logistic regression)

  • 강명욱;신은영
    • Journal of the Korean Data and Information Science Society
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    • 제23권1호
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    • pp.99-111
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    • 2012
  • 반응변수가 주어졌을 때 설명변수의 조건부 확률분포의 로그-밀도비는 로지스틱회귀모형에서 어떤 설명변수가 어떻게 모형에 포함되는지에 대한 변수선택문제에서 유용한 정보를 제공한다. 설명변수의 조건부 확률분포가 좌우대칭이 아닌 경우 감마분포로 가정하는 것이 적절하고 이 경우 x항과 log(x)항이 모형에 포함되어야 한다. 로그-오즈 그래프는 변수선택문제를 연구하는데 매우 중요한 도구가 된다. 이러한 그래픽적 연구에 의하면, x|y = 0과 x|y = 1의 두 분포가 겹치는 경우에서는 x항과 log(x)항 모두 필요하다. 그리고 두 분포가 분리된 경우에는 x항 또는 log(x)항 중 하나만 필요하다.

Robust optimization of reinforced concrete folded plate and shell roof structure incorporating parameter uncertainty

  • Bhattacharjya, Soumya;Chakrabortia, Subhasis;Dasb, Subhashis
    • Structural Engineering and Mechanics
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    • 제56권5호
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    • pp.707-726
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    • 2015
  • There is a growing trend of considering uncertainty in optimization process since last few decades. In this regard, Robust Design Optimization (RDO) scheme has gained increasing momentum because of its virtue of improving performance of structure by minimizing the variation of performance and ensuring necessary safety and feasibility of constraint under uncertainty. In the present study, RDO of reinforced concrete folded plate and shell structure has been carried out incorporating uncertainty in the relevant parameters by Monte Carlo Simulation. Folded plate and shell structures are among the new generation popular structures often used in aesthetically appealing constructions. However, RDO study of such important structures is observed to be scarce. The optimization problem is formulated as cost minimization problem subjected to the force and displacements constraints considering dead, live and wind load. Then, the RDO is framed by simultaneously optimizing the expected value and the variation of the performance function using weighted sum approach. The robustness in constraint is ensured by adding suitable penalty term and through a target reliability index. The RDO problem is solved by Sequential Quadratic Programming. Subsequently, the results of the RDO are compared with conventional deterministic design approach. The parametric study implies that robust designs can be achieved by sacrificing only small increment in initial cost, but at the same time, considerable quality and guarantee of the structural behaviour can be ensured by the RDO solutions.

Analysis of Solar and Lunar Motions in the Seonmyeong Calendar

  • Lee, Ki-Won
    • Journal of Astronomy and Space Sciences
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    • 제36권2호
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    • pp.87-96
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    • 2019
  • We investigate solar and lunar motions in the Seonmyeong (SM) calendar that was compiled by Xu, Ang of the Tang dynasty (A.D. 618-907) in China and used for 71 years from 822 to 892. This calendar was also used in Korea during the Goryeo dynasty (A.D. 918-1392) and in Japan for 823 years from 862 to 1684, the longest time among the three countries. Referring to historical documents of China, Korea, and Japan, we analyze the calendrical methods of calculating the daily apparent movements of the Sun and Moon in the SM calendar, which were considered their unequal motions, and compare the movements with the results of modern calculations for three periods in the Goryeo dynasty: 919, 1155, and 1392 years (i.e., the beginning, middle, and ending of the dynasty, respectively). We find that a quadratic equation was employed to obtain the daily movement of the Sun using physical quantities on the instant of each solar term, which was tabulated in its calendar book such as the Goryeosa (History of the Goryeo Dynasty). For quantitative analysis, we compute the mean absolute difference (MAD) of the daily apparent movement between the SM calendar and modern calculations and obtain 0.33, 0.30, and 0.31 arcmin for the periods of 919, 1155, and 1392 years, respectively. Meanwhile, we find relatively large MAD values in the daily movement of the Moon: 0.217, 0.284, and 0.240 degrees for each corresponding year. An interesting point is that the MAD value in the lunar motion shows the maximum in 1155 years, and is the minimum in the solar motion. In conclusion, we believe that this study will facilitate in the understanding of the SM calendar further, particularly in the calendrical methods of calculating sunrise, sunset, and eclipse times.

열오염 혼합 거동 해석을 위한 수평 2차원 유한요소모형 (Horizontal 2-D Finite Element Model for Analysis of Mixing Transport of Heat Pollutant)

  • 서일원;최황정;송창근
    • 대한토목학회논문집
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    • 제31권6B호
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    • pp.507-514
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    • 2011
  • 본 논문에서는 하천에 유입되는 열 오염물질의 혼합거동을 분석하기 위해 2차원 수심 평균된 이송-분산방정식에 유한요소법을 적용하여 수치 모형을 개발하였다. 유한요소법의 여러 수치기법 중 SUPG법을 적용하였으며, 복잡한 하천경계를 보다 정확히 재현할 수 있도록 삼각 및 사각 요소망의 혼용이 가능하도록 하였다. 열 오염물질의 거동을 표현하기 위해서 열 교환을 묘사하는 반응항을 평형온도와 수온과의 차이에 비례하는 식으로 나타내고, 열교환 계수 및 평형온도에 따라 수온의 변화가 적용되도록 방정식을 구성하였다. 모형의 검증을 위하여 직사각형 수로에 선원으로 연속주입하여 얻은 수치해와 1차원 정상상태의 해석해를 비교하였다. 비교결과 수치해와 해석해의 결과가 서로 일치하는 것으로 밝혀졌다. 모형의 현장적용을 위해 상수원 보호구역인 팔당댐 하류부터 잠실수중보까지 22.5 km 구간을 대상영역으로 하였다. 구리하수처리장 방류수에 의한 수온 변화를 모의한 결과 수질측정망 측정자료와 비교적 비슷한 경향이 나타났다. 본 연구에서 개발한 수치모형이 열 오염원 유입으로 인한 수온 변화를 잘 표현하는 것을 알 수 있었다.

2차원 및 3차원 동적복합조석모형에 의한 경남해역의 조석산정 (Computation of Tides for Off Kyungnam Coast with Dynamically Combined Two-Dimensional and Three-Dimensional Tidal Model)

  • 최병호;우승범
    • 한국해안해양공학회지
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    • 제7권2호
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    • pp.176-197
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    • 1995
  • 한국경남해역의 2차원 및 3차원적 조류구조를 동적원리에 근거한 수치모형을 통하여 조사하였다. 2차원 수치모형을 이용하여 주 8개 분조(M$_2$, S$_2$, $K_1$, $O_1$, $N_2$, $K_2$, P$_1$, Q$_1$)에 대한 조석체계를 계산하였다. 계산결과는 해안의 관측치와 비교하여 만족할만한 일치를 보였다. 이러한 결과를 토대로 하여 매년 적조등으로 인해 심각한 오염이 발생되고 있는 진해만과 마산만의 3차원적 조석순환구조를 조사하기 위하여 기 수립된 2차원 모형과 내만의 3차원 모형을 연결시키도록 개선하였다. 그 방법으로 Davies(1980)가 제시한 2차원 수심적분 모형과 3차원 Galerkin-Spectral 모형과의 동적연결방법을 이용하였다. Davies의 연구에 추가하여 본 연구에서는 3차원 수치모형에 자승형마찰항과 비선형 이류항을 추가하였다. 3차원 모형에서 산정된 각 수심별 M$_2$ 분조의 조류타원도는 KORDI(1990)가 수행한 수심별 조류관측치와 양호한 일치를 보였다.

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The Effect of Export on R&D Cost Behavior: Evidence from Korea

  • Chang Youl Ko;Hoon Jung
    • Journal of Korea Trade
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    • 제26권5호
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    • pp.23-38
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    • 2022
  • Purpose - This research intends to find out whether R&D cost stickiness shows differentiated aspects depending on exports in Korea. A cost behavior that indicates a lower rate of costs decrease when sales decrease than the rate of costs increase when sales increase is called cost stickiness. This sticky cost behavior is caused by considering the adjusting costs. This study aims to empirically verify that R&D cost stickiness is greater in export firms than in non-export firms. We also investigate the effect of exports on R&D cost stickiness is nonlinear. Design/methodology - We obtain data for the analysis from Kis-Value and TS2000 from 2012 to 2020. This study tests for R&D cost stickiness of exports using the cost stickiness model developed by Anderson et al. (2003) that is used in a lot of prior literature. To explore the nonlinear behavior of R&D cost stickiness we include a quadratic term of exports in our model. Findings - The results of our analysis are as follows. First, we observed that R&D costs of export firms are more sticky than that of non-export firms. Our result indicated that export firms are less likely to reduce R&D costs in decreasing sales periods in preparation for future sales recovery. Second, our empirical evidence shows that export firms view R&D costs much favorably. However, we hypothesize that the effect of export intensity on R&D costs may not necessarily be linear. Our result shows the effect of exports intensity on R&D stickiness is thus nonlinear, forming a reverse U-shaped curve. When export intensity exceeds a certain threshold, the growth rate of R&D costs appears to be viewed negatively. Firms with relatively high export intensity do not support R&D costs, viewing them as taking away firms' resources from other more productive costs. On the contrary, those with export intensity under the threshold view R&D costs as beneficial and therefore promote further R&D costs when revenue decreases. Originality/value - The results of this research can contribute academically to the expansion of empirical research on R&D cost stickiness. R&D cost stickiness varies by industry. As a result of our research, the managers of export firms recognize the importance of R&D to lead innovation. We expected that this research contributes to further studies on R&D costs and cost stickiness. Second, this research has implications from a business perspectives. Our findings of export firms' R&D stickiness suggest that export firms' managers should consider keeping the stickiness of R&D when revenue decreases because it is essential for exporting firms to maintain their R&D stickiness to secure long-term competitiveness. R&D stickiness can be used on a practical basis to emphasize the need for continuous investment in exporting firms' R&D activities.

Photo-Fenton 산화공정에서 반응표면분석법을 이용한 축산폐수의 COD 처리조건 최적화 및 예측식 수립 (Optimization and Development of Prediction Model on the Removal Condition of Livestock Wastewater using a Response Surface Method in the Photo-Fenton Oxidation Process)

  • 조일형;장순웅;이시진
    • 대한환경공학회지
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    • 제30권6호
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    • pp.642-652
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    • 2008
  • 본 연구는 축산폐수 중 COD$_{Cr}$을 응집공정 후 Photo-Fenton 공정에 의해 산화분해 최적조건 및 제거 예측식에 수립에 관한 연구이다. 본 연구는 축산폐수 중 COD$_{Cr}$에 대한 Photo-Fenton 산화반응을 이용하여 이들 분해특성을 2차원 반응모델로 추정하기 위해 중심합설계법 대안으로 많이 사용되고 있는 박스-벤켄법(Box-Behnken method)을 이용하였다. 최적조건 수립을 위한 입력변수, 즉 3가지 변수(Fe(II)(x$_1$), $H_2O_2(x_2)$, pH(x$_3$)) 등을 램덤화, 반복화 및 블록화 원리에 따라 실험설계하여 반응값에 대한 예측식을 수학적으로 산출하였다. 수학적 및 통계적으로 산출된 예측식은 Y = 79.3 + 15.61x$_1$ - 7.31x$_2$ - 4.26x$_3$ - 18x$_1{^2}$ - 10x$_2{^2}$ - 11.9x$_3{^2}$ + 2.49x$_1x_2$ - 4.4x$_2x_3$ - 1.65x$_1x_3$와 같이 얻을 수 있었고 COD$^{Cr}$ 제거율(%)의 실측치에 대한 예측치의 적합도(goodness of fit) 검증시 결정계수(coefficient of determination: R$^2$) 0.96으로 에측식을 충분히 설명할 수 있었다. 예측 모형에 대한 최소제곱추정법으로 적합된 반응표면에서 1차 선형항(linear term)은 Fe(II)(x$_1$), $H_2O_2(x_2)$, 그리고 pH(x$_3$)은 상승작용(synergistic effect)으로 반응모델에 유의한 차이를 보였으며(p < 0.001) 그러나 교호항(cross-product term)은 $H_2O_2$ $\times$ pH(x$_2x_3$)와 순수이차항(quadratic terms)의 Fe(II) $\times$ Fe(II)(x$_1{^2}$), $H_2O_2$ $\times$ H$_2O_2$(x$_2{^2}$) 그리고 pH $times$ pH(x$_3{^2}$) 등은 대립적인(감쇠)(antagonistic effect) 작용으로 반응모델에 유의한 차이를 보였다(p < 0.01). 반응 모델에 대한 예측식 수립 후 COD$_{Cr}$ 제거율(%)의 최적조건을 도출하기 위해 정준분석(canonical analysis)와 능선분석(ridge analysis)에 이용한 결과 반응값(결과값: Y)은 84 $\pm$ 0.95%, COD$_{Cr}$ 최적처리를 위한 변수들의 조건은 Fe(II)(X$_1$) = 0.0146 mM, $H_2O_2$(X$_2$) = 0.0867 mM 그리고 pH(X$_3$) = 4.704 등의 결과를 얻을 수 있었다. 또한 이들 최적조건을 이용하여 재현성을 통한 모델검증 결과 높은 신뢰성을 보였다.