• Title/Summary/Keyword: Rosenbrock

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Pyrolysis Reaction for the Treatment of Hazardous Halogenated Hydrocarbon Waste (유해 할로겐화 탄화수소 폐기물 처리를 위한 열분해 반응)

  • 조완근
    • Journal of Environmental Science International
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    • v.6 no.4
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    • pp.399-407
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    • 1997
  • The pyrolysis reactions of atomic hydrogen with chloroform were studied In a 4 cm 1.6. tubular flow reactor with low flow velocity 1518 cm/sec and a 2.6 cm 1.4. tubular flow reactor with high flow velocity (1227 cm/sec). The hydrogen atom concentration was measured by chemiluminescence titration with nitrogen dioxide, and the chloroform concentrations were determined using a gas chromatography. The chloroform conversion efficiency depended on both the chloroform flow rate and linear flow velocity, but 416 not depend on the flow rate of hydrogen atom. A computer model was employed to estimate a rate constant for the initial reaction of atomic hydrogen with chloroform. The model consisted of a scheme for chloroform-hydrogen atom reaction, Runge-Kutta 4th-order method for Integration of first-order differential equations describing the time dependence of the concentrations of various chemical species, and Rosenbrock method for optimization to match model and experimental results. The scheme for chloroform-hydrogen atom reaction Included 22 elementary reactions. The rate constant estimated using the data obtained from the 2.6 cm 1.4. reactor was to be 8.1 $\times$ $10^{-14}$ $cm^3$/molecule-sec and 3.8 $\times$ $10^{-15}$ cms/molecule-sec, and the deviations of computer model from experimental results were 9% and 12% , for the each reaction time of 0.028 sec and 0.072 sec, respectively.

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Parameter Optimization and Uncertainty Analysis of the Rainfall-Runoff Model Coupled with Hierarchical Bayesian Inference Scheme (Hierarchical Bayesian 기법을 통한 강우-유출모형 매개변수의 최적화 및 불확실성 분석)

  • Mun, Yeong-Il;Gwon, Hyeon-Han
    • Proceedings of the Korea Water Resources Association Conference
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    • 2007.05a
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    • pp.1752-1756
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    • 2007
  • 정교한 강우-유출 모의를 위해서는 적절한 매개변수의 추정이 필수적이며, 매개변수 추정 방법은 시행착오(trial and error)에 의한 수동보정법과 최적화방법을 사용한 자동보정법으로 구분할 수 있다. 모형의 매개변수의 수가 많은 경우 수동보정법에 의한 매개변수 추정은 매우 어렵다. 자동 보정법에 사용되는 최적화방법은 Rosenbrock 알고리즘, patten search, 컴플렉스(complex) 방법, Powell 방법 등과 같은 지역최적화 방법과 전역최적화 방법으로 나눌 수 있다. 그러나 기존 방법론들은 매개변수의 최적화를 추적하기 위한 알고리즘이 대부분이며 이들 매개변수에 관련된 불확실성을 평가하는데는 미흡한 단접이 있다. 이러한 점에서 본 연구에서는 강우-유출모형의 매개변수 추정에 있어서 불확실성을 평가할 수 있는 새로운 방법론을 검토하고자 한다. 매개변수와 관련된 불확실성을 평가하기 위한 방법은 여러 가지가 있으나 통계적으로 매우 우수한 능력을 보이는 Hierarchical Bayesian 알고리즘을 Probability-Distributed 강우-유출 모형에 적용하였다. 본 방법론은 최적화와 동시에 각 매개변수에 관련된 사후분포(posterior distribution)의 추정이 가능하므로 모형이 갖는 불확실성을 효과적으로 평가할 수 있다. 따라서, 수자원 관리에 있어서 불확실성을 고려할 수 있으므로 보다 수리수문학적 위험도를 저감할 수 있을 것으로 판단된다.

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A Study on the Application of Thomas Monthly Runoff Prediction Model for Ungauged Watersheds (Thomas 월 유출모형의 미계측 영역 적용에 관한 연구)

  • 김원석;윤용남;최영박
    • Water for future
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    • v.24 no.4
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    • pp.85-91
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    • 1991
  • An effort was made to develop a monthly runoff predition method based on the Thomas model. For the 20watersheds selected the Thomas model was fitted, the parameters being determined by the Rosenbrok's rotating coordinate search method using the monthly rainfall and runoff data. The so determined parameters were correlated with the meteorologic, topographic and geologic characteristics of the watersheds. The model was tested by comparing the observed and simulated monthly runoff records from two test watersheds. The result showed that the model developed in the present study could satisfactorily be applied to ungauged watersheds It was noticed that the model had the tendency of slightly overestimating the runoff during winter periond and underestimating during the spring period.

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Load rating of box girder bridges based on rapid testing using moving loads

  • Hong Zhou;Dong-Hui Yang;Ting-Hua Yi;Hong-Nan Li
    • Smart Structures and Systems
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    • v.32 no.6
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    • pp.371-382
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    • 2023
  • Box girder bridges are now widely used in bridge construction, and it is necessary to perform load rating regularly to evaluate the load capacity of box girder bridges. Load testing is a common measure for load rating. However, the bridge must be loaded by many trucks under different loading conditions, which is time-consuming and laborious. To solve this problem, this paper proposes a load rating method for box girder bridges based on rapid moving loads testing. The method includes three steps. First, the quasi-influence factors of the bridge are obtained by crossing the bridge with rapidly moving loads, and the structural modal parameters are simultaneously obtained from the dynamic data to supplement. Second, an objective function is constructed, consisting of the quasi-influence factors at several measurement points and structural modal parameters. The finite element model for load rating is then updated based on the Rosenbrock method. Third, on this basis, a load rating method is proposed using the updated model. The load rating method proposed in this paper can considerably reduce the time duration of traditional static load testing and effectively utilize the dynamic and static properties of box girder bridges to obtain an accurate finite element model. The load capacity obtained based on the updated model can avoid the inconsistency of the evaluation results for the different structural members using the adjustment factors specified in codes.

Long-term runoff characteristics on HRU variations of PRMS (PRMS의 HRU크기에 따른 장기유출특성)

  • Kim, Nam-Won;Kim, Hyeon-Jun;Park, Sun-Ho
    • Journal of Korea Water Resources Association
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    • v.38 no.2
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    • pp.167-177
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    • 2005
  • In this study, the PRMS(Precipitation and Runoff Modeling System), developed by USGS(United States Geological Survey), was applied to the Yongdam dam watershed in the Geum River basin. The efficiency for runoff simulation and spatial characteristics of PRMS were evaluated. The runoff changes with the changes of subcatchments and HRUs were estimated. As results, the size of the subcatchment and HRV did not significantly affect the runoff at the exit of watershed. Consequently, the spatial characteristic of PRMS was shown as lumped type rather than semi-distributed. The geographical input data for Yongdam dam watershed were converted to the USGS Input type, and the parameters were calibrated using Rosenbrock optimization method, validated with the observed runoff data. The PRMS showed resonable agreements in the long-term continuous runoff simulation, if the accuracy of observed data is ensured.

Numerical assessment of step-by-step integration methods in the paradigm of real-time hybrid testing

  • Verma, Mohit;Rajasankar, J.;Iyer, Nagesh R.
    • Earthquakes and Structures
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    • v.8 no.6
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    • pp.1325-1348
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    • 2015
  • Real-time hybrid testing (RTHT) involves virtual splitting of the structure into two parts: physical substructure that contains the key region of interest which is tested in a laboratory and numerical substructure that contains the remaining part of the structure in the form of a numerical model. This paper numerically assesses four step-by-step integration methods (Central difference method (CDM), Operator splitting method (OSM), Rosenbrock based method (RBM) and CR-integration method (CR)) which are widely used in RTHT. The methods have been assessed in terms of stability and accuracy for various realistic damping ratios of the physical substructure. The stability is assessed in terms of the spectral radii of the amplification matrix while the accuracy in terms of numerical damping and period distortion. In order to evaluate the performance of the methods, five carefully chosen examples have been studied - undamped SDOF, damped SDOF, instantaneous softening, instantaneous hardening and hysteretic system. The performance of the methods is measured in terms of a non-dimensional error index for displacement and velocity. Based on the error indices, it is observed that OSM and RBM are robust and performs fairly well in all the cases. CDM performed well for undamped SDOF system. CR method can be used for the system showing softening behaviour. The error indices indicate that accuracy of OSM is more than other method in case of hysteretic system. The accuracy of the results obtained through time integration methods for different damping ratios of the physical substructure is addressed in the present study. In the presence of a number of integration methods, it is preferable to have criteria for the selection of the time integration scheme. As such criteria are not available presently, this paper attempts to fill this gap by numerically assessing the four commonly used step-by-step methods.

Implicit Large Eddy Simulations of a rectangular 5:1 cylinder with a high-order discontinuous Galerkin method

  • Crivellini, Andrea;Nigro, Alessandra;Colombo, Alessandro;Ghidoni, Antonio;Noventa, Gianmaria;Cimarelli, Andrea;Corsini, Roberto
    • Wind and Structures
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    • v.34 no.1
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    • pp.59-72
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    • 2022
  • In this work the numerical results of the flow around a 5:1 rectangular cylinder at Reynolds numbers 3 000 and 40 000, zero angle of attack and smooth incoming flow condition are presented. Implicit Large Eddy Simulations (ILES) have been performed with a high-order accurate spatial scheme and an implicit high-order accurate time integration method. The spatial approximation is based on a discontinuous Galerkin (dG) method, while the time integration exploits a linearly-implicit Rosenbrock-type Runge-Kutta scheme. The aim of this work is to show the feasibility of high-fidelity flow simulations with a moderate number of DOFs and large time step sizes. Moreover, the effect of different parameters, i.e., dimension of the computational domain, mesh type, grid resolution, boundary conditions, time step size and polynomial approximation, on the results accuracy is investigated. Our best dG result at Re=3 000 perfectly agrees with a reference DNS obtained using Nek5000 and about 40 times more degrees of freedom. The Re=40 000 computations, which are strongly under-resolved, show a reasonable correspondence with the experimental data of Mannini et al. (2017) and the LES of Zhang and Xu (2020).

A Study on Shape Optimization of Plane Truss Structures (평면(平面) 트러스 구조물(構造物)의 형상최적화(形狀最適化)에 관한 구연(究研))

  • Lee, Gyu won;Byun, Keun Joo;Hwang, Hak Joo
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.5 no.3
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    • pp.49-59
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    • 1985
  • Formulation of the geometric optimization for truss structures based on the elasticity theory turn out to be the nonlinear programming problem which has to deal with the Cross sectional area of the member and the coordinates of its nodes simultaneously. A few techniques have been proposed and adopted for the analysis of this nonlinear programming problem for the time being. These techniques, however, bear some limitations on truss shapes loading conditions and design criteria for the practical application to real structures. A generalized algorithm for the geometric optimization of the truss structures which can eliminate the above mentioned limitations, is developed in this study. The algorithm developed utilizes the two-phases technique. In the first phase, the cross sectional area of the truss member is optimized by transforming the nonlinear problem into SUMT, and solving SUMT utilizing the modified Newton-Raphson method. In the second phase, the geometric shape is optimized utilizing the unidirctional search technique of the Rosenbrock method which make it possible to minimize only the objective function. The algorithm developed in this study is numerically tested for several truss structures with various shapes, loading conditions and design criteria, and compared with the results of the other algorithms to examme its applicability and stability. The numerical comparisons show that the two-phases algorithm developed in this study is safely applicable to any design criteria, and the convergency rate is very fast and stable compared with other iteration methods for the geometric optimization of truss structures.

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Generation of High Resolution Scenarios for Climate Change Impacts on Water Resources (II): Runoff Scenarios on Each Sub-basins (수자원에 대한 기후변화 영향평가를 위한 고해상도 시나리오 생산(II): 유역별 유출시나리오 구축)

  • Jung, Il-Won;Bae, Deg-Hyo;Im, Eun-Soon
    • Journal of Korea Water Resources Association
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    • v.40 no.3
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    • pp.205-214
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    • 2007
  • The objective of this study is to generate the regional scale runoff scenarios by using IPCC SRES A2 climate change scenario for analyzing the spatial variation of water resources in Korea. The PRMS model was adopted to simulate long-term stream discharge. To estimate the PRMS model parameters on each sub-basin, the streamflow data at 6 dam sites and Rosenbrock's scheme are used for model parameter calibration and those parameters are translated to ungauged catchments by regionalization method. The other 3 dam sites are selected for the verification of the adequateness of regionalized model parameters in ungagued catchments. The statistical results show that the simulated flows by using regionalized parameters well agree with observed ones. The generated runoff scenarios by climate change are compared with observed data on 4 dam sites for the reference period. The consequences show that the selection of climate station for generating climate scenario affects the reliability of climate scenario at sub-basin. The comparison results of the stream flows between the 30-year baseline period (1971-2000) and future 90-year (2001-2030, 2031-2060, 2061-2090) show that the long-term mean annual runoff in the Han River has increasing trend, while the Nakdong, the Gum, the Youngsan and the Sumjin Rivers have decreasing trend.