적응 벌칙함수와 집합체 혼합진화 기법의 결합 및 유역유출 모형의 매개변수 추정에 대한 적용

Abstract

Evolutionary algorithms commonly used for an automatic calibration of watershed runoff simulation models are unconstrained optimization algorithms. A watershed runoff phenomenon, on the other hand, is so complicated there are some limitations to calibrate a watershed runoff model only with a single objective function. Many researchers have used multiple objective functions for parameter estimation of watershed runoff simulation models to overcome the limitations of single objective functions. Application of the multiple objective functions, however, has some difficulties in determination of weights for objective functions and in selection of a solution from many optimal solutions such as the Pareto optimum. The purpose of this study is to develop an optimization module to overcome the limitations and difficulties for the above parameter estimation methods of the watershed runoff simulation models. An adaptive penalty function was used to impose constraints on the model calibration process and it was embedded in the shuffled complex evolution-University of Arizona (SCE-UA) optimization program. The adaptive penalty function is easily implemented, free of parameter tuning, and guaranteed to find a solution for any problem at every run. The modified SCE-UA was validated through the applications to the three constrained optimization problems. And then an automatic calibration module for the SWMM (storm water management model) was developed by linking the modified SCE-UA with the SWMM. The automatic calibration module was applied to the parameter estimations for watershed runoff event simulations and watershed runoff continuous simulations. Some limitations were revealed from the results of the automatic calibrations for the two types of simulations with a single objective function. The constraints were formulated to overcome the limitations according to the type of watershed runoff simulation. Two constraints are imposed to diminish errors of peak flow and peak time on the watershed runoff event simulation. Reducing errors of high and low flow volumes formed two constraints to improve water balance on the watershed runoff continuous simulation. The automatic calibration results with those constraints showed great improvement in reducing errors of peak flow and peak flow occurrence time. The shape of the flood hydrograph was more similar to the observed hydrograph than that of automatic calibration results without the constraints. Water balance was also somewhat improved in the watershed runoff continuous simulation by including the constraints. The verification results from the automatic calibration imposing the constraints were better than those of the automatic calibration without the constraints. The constrained optimization module developed by embedding the adaptive penalty function could help solving various constrained optimization problems in water resources engineering fields.