Robust parameter set selection of unsteady flow model using Pareto optimums and minimax regret approach

Li Li; Eun-Sung Chung; Kyung Soo Jun

doi:10.3741/JKWRA.2017.50.3.191

All Issue

2017 Vol.50, Issue 3 Preview Page Next Page

Robust parameter set selection of unsteady flow model using Pareto optimums and minimax regret approach 파레토 최적화와 최소최대 후회도 방법을 이용한 부정류 계산모형의 안정적인 매개변수 추정

31 March 2017. pp. 191-200

PDF XML

Abstract

A robust parameter set (ROPS) selection framework for an unsteady flow model was developed by combining Pareto optimums obtained by outcomes of model calibration using multi-site observations with the minimax regret approach (MRA). The multi-site calibration problem which is a multi-objective problem was solved by using an aggregation approach which aggregates the weighted criteria related to different sites into one measure, and then performs a large number of individual optimization runs with different weight combinations to obtain Pareto solutions. Roughness parameter structure which can describe the variation of Manning’s n with discharges and sub-reaches was proposed and the related coefficients were optimized as model parameters. By applying the MRA which is a decision criterion, the Pareto solutions were ranked based on the obtained regrets related to each Pareto solution, and the top-rated one due to the lowest aggregated regrets of both calibration and validation was determined as the only ROPS. It was found that the determination of variable roughness and the corresponding standardized RMSEs at the two gauging stations varies considerably depending on the combinations of weights on the two sites. This method can provide the robust parameter set for the multi-site calibration problems in hydrologic and hydraulic models.

Keywords

Minimax regret approach

Pareto optimum

Robust parameter set selection

Unsteady flow model

Variable roughness coefficient

본 연구에서는 부정류 계산모형의 안정적인 매개변수를 선정하기 위하여, 다수 지점의 관측치를 고려한 모형보정의 결과로부터 얻은 파레토 최적화와 최소최대 후회도 방법(minimax regret approach, MRA)을 결합하는 방법을 제안하였다. 여러 지점의 관측치를 고려한 모형의 보정은 다목적 최적화 문제로서, 통합접근법을 적용하여 최적해를 구하였다. 통합접근법은 여러 지점에 대한 가중치를 결합하여 하나의 목적함수를 얻고, 여러 번의 개별 최적화를 수행함으로써 다수의 파레토 최적해들을 구하는 방법이다. 이때 유량에 따른 조도계수의 가변성을 나타내는 두 개의 매개변수로 구성된 관계식을 이용하여 두 구간에 대한 매개변수들을 모형의 추정 대상 매개변수로서 최적화하였다. 이후 각기 다른 홍수사상에 대해 보정과 검증을 수행하였으며 각각에 대한 평가지표의 후회도를 정량화하였고 이를 결합한 결합후회도를 산정하였다. 이를 기준으로 파레토 최적해들의 순위를 결정하였다. 계산결과 추정된 모형의 가변조도계수와 그로부터 얻은 두 개 지점에서의 표준화된 RMSE들은 두 지점에 대한 가중치의 조합에 따라 선택되는 매개변수 값에 따라 달라짐을 알 수 있었다. 본 연구에서 제시한 방법은 수문 및 수리모형의 다수의 관측지점의 자료를 이용한 매개변수 산정문제에 있어서 안정적인 해를 도출할 수 있다.

키워드

최소최대 후회도방법

파레토 최적해

안정적 매개변수 선정

부정류 계산모형

가변 조도계수

References

Ministry of Construction and Transportation (MOCT) (2002). “Han River Master Plan Report” Technical Report.

Atanov, G. A., Evseeva, E. G., and Meselhe E. A. (1999). “Estimation of roughness profile in trapezoidal open channel.” J. Hydraul. Eng., Vol. 125, No. 3, pp. 309-312.

Chow, V. T. (1959). Open channel hydraulics. McGraw-Hill, New York.

Chung, E. S., and Kim, Y. (2014). “Development of fuzzy multi- criteria approach to prioritize locations of treated wastewater use considering climate change scenarios.” J. Environ. Manag., Vol. 146, pp. 505-516.

Coon, W. F. (1998). “Estimation of roughness coefficients for natural stream channels with vegetated banks.” U.S. Geological Survey Water-Supply Paper, Vol. 2441, pp. 133.

Cunge, J. A., Holly, F. M., and Verwey, A. (1980). Practical aspects of computational river hydraulics. Pitman.

Dung, N. V., Merz, B., Bardossy, A., Thang, T. D., and Apel, H. (2011). “Multi-objective automatic calibration of hydrodynamic models utilizing inundation maps and gauge data.” Hydrol. Earth Syst. Sci., Vol. 15, pp. 1339-1354.

Holly, F. M., Yang, J. C., Schwarz, P., Schaefer, J., Hsu, S. H., and Einhellig, R. (1990). “Numerical simulation of unsteady water and sediment movement in multiply connected networks of mobile-bed Channels.” IIHR Report, No. 343, Iowa Inst. of Hydr. Res., Iowa.

Horritt, M. S. (2000). “Calibration of a two-dimensional finite element flood flow model using satellite imagery.” Water Resour. Res., Vol. 36, No. 11, 3279-3291.

Hunter, N. M., Bates, P. D., Horritt, M. S, De Roo, A. P. J., and Werner, M. G. F. (2005). “Utility of different data types for calibrating flood inundation models within a GLUE framework.” Hydrol. Earth. Syst. Sci., Vol. 9, No. 4, pp. 412-430.

Hwang, E. J., and Jun, K. S. (1997). “Unsteady flow model for the Main Reach of the Han River: Calibration.” Korea Water Resources Association, Vol. 30, No. 5, pp. 549-559.

Jun, K. S. (1996). “A study on unsteady flow model including weir flow simulation.” J. Korea Water Resources Association, Vol. 29, No. 2, pp. 153-165.

Khatibi, R. H., Williams, J. J. R., and Wormleaton, P. R. (1997). Identification problem of open-channel friction parameter. J. Hydraul. Eng., Vol. 123, No. 12, pp. 1078-1088.

Khu, S. T., and Madsen, H. (2005). “Multiobjective calibration with Pareto preference ordering: An application to rainfall-runoff model calibration.” Water Resour. Res., Vol. 41, No. W03004.

Kim, H. J., and Jun, K. S. (2004). “Unsteady flow model with variable roughness coefficient” Korea Water Resources Association, Vol. 37, No. 12, pp. 1055-1063.

Kim, Y., and Chung, E. S. (2014). “An index-based robust decision making framework for watershed management in a changing climate.” Sci. Tot. Environ., Vol. 473, pp. 88-102.

Kim, Y., Chung, E. S., and Jun, S. (2015a). “Iterative framework for robust reclaimed wastewater allocation in a changing environment using multi-criteria decision making.” Water Resour. Manage., Vol. 29, No. 2, pp. 295-311.

Kim, Y., Chung, E. S., Won, K. J., and Gil, K. I. (2015b). “Robust parameter estimation framework of a rainfall-runoff model using pareto optimum and minimax regret approach.” Water, Vol. 7, pp. 1246-1263.

Liggett, J. A., and Cunge, J. A. (1975). “Numerical methods of solution of the unsteady flow equations.” In: Mohmmod, K., Yevjevich, V. (eds.), Unsteady flow in open channels, Water Resour. Publications, Fort Collins, Colo., pp. 89-182.

Liu, Y. B., Batelaan, O., De Smedt, F., Poórová, J., and Velcická, L. (2005). “Automated calibration applied to a GIS-based flood simulation model using PEST.” In: van Alphen, J., van Beek, E., Taal, M. (eds.), Floods, from Defence to Management, Taylor-Francis Group, London, pp. 317-326.

Loomes, G., and Sugden, R. (1982). “Regret theory: An alternative theory of rational choice under uncertainty.", Econ. J., Vol. 92, No. 4, pp. 805-824.

Loulou, R., and Kanudia, A. (1999). “Minimax regret strategies for greenhouse has abatement: Methodology and application.” Oper. Res. Lett., Vol. 25, pp. 219-230.

Ramesh, R., Datta, B., Bhallamudi, S. M., and Narayana, A. (2000). “Optimal estimation of roughness in open-channel flows.” J. Hydraul. Eng., Vol. 126, No. 4, pp. 299-303.

Rouse, H. (1965). “Critical analysis of open channel resistance.” J. Hydraul. Div., Vol. 91, No. HY4, pp. 1-25.

Seibert, J., Uhlenbrook, S., Leibundgut, C., and Haldin, S. (2000). “Multiscale calibration and validation of a conceptual rainfall- runoff model.” Phys. Chem. Earth, Vol. 25, No. 1, pp. 59-64.

Shinma, T. A., and Reis, L. F. R. (2014). “Incorporating multi-event and multi-site data in the calibration of SWMM.” Proc. Eng., Vol. 79, pp. 75-84.

Stevenson, W. J., and Ozgur, C. 2007. Introduction to management science with spreadsheets. McGraw-Hill, New York.

Information

Publisher :KOREA WATER RESOURECES ASSOCIATION
Publisher(Ko) :한국수자원학회
Journal Title :Journal of Korea Water Resources Association
Journal Title(Ko) :한국수자원학회 논문집
Volume : 50
No :3
Pages :191-200
Received Date : 2017-01-21
Revised Date : 2017-02-20
Accepted Date : 2017-02-28
DOI :https://doi.org/10.3741/JKWRA.2017.50.3.191

Journal of Korea Water Resources Association ISSN:2799-8746(Print) 2799-8754(Online) 한국수자원학회 논문집

All Issue