Journal of Korea Water Resources Association (한국수자원학회논문집)

Korea Water Resources Association (한국수자원학회)
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Application of Levenberg Marquardt Method for Calibration of Unsteady Friction Model for a Pipeline System

관수로 부정류 마찰항 보정을 위한 Levenberg Marquardt 방법의 적용연구

  • 박조은 (부산대학교 대학원 환경공학과) ;
  • 김상현 (부산대학교 환경공학과)
  • Received : 2012.10.15
  • Accepted : 2013.01.07
  • Published : 2013.04.30
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Abstract

In this study, a conventional pipeline unsteady friction model has been integrated into Levenberg Marquardt method to calibrate friction coefficient in a pipeline system. The method of characteristics has been employed as the modeling platform for the frequency dependant model of unsteady friction. In order to obtain Hessian and Jacobian matrix for optimization, the direct differentiation of pressure to friction factor was calculated and sensitivities to friction for heads and discharges were formulated for implementation to the integration constant in the characteristic method. Using a hypothetical simple pipeline system, time series of pressure, introduced by a sudden valve closure, were obtained for various Reynolds numbers. Convergency in fiction factors were evaluated both in steady and unsteady friction models. The comparison of calibration performance between the proposed method and genetic algorithm indicates that faster and stabler behaviour of Levenberg Marquardt method than those of evolutionary calibration.

이 논문에서는 관망시스템의 마찰항을 보정하기 위해서, 부정류 마찰 모형과 Levenberg Marquardt 방법을 합성하였다. 부정류 마찰항을 고려하기 위한 방법으로 빈도 의존 마찰항을 사용하였으며, 특성선 방법을 모형 개발의 기반으로 하였다. 최적화에 필요한 Hessian과 Jacobian 행렬을 구하기위해서 수압을 직접 마찰항에 미분한 항을 계산하였으며, 특성선 방법상에서의 다양한 수압과 유량에 대한 마찰계수의 민감도를 수식으로 유도하였다. 간단한 관망을 가정한 뒤, 갑작스런 밸브의 거동으로 도입된수압의 시계열을 확보하였고, 이를 이용하여 정상류 마찰 모형과 부정류 마찰모형의 마찰항 보정을 수행하였다. 제안된 방법과 진화 연산 알고리즘의 마찰항 수렴거동을 비교하였으며, Leveberg Marquardt 방법의 안정적이고 신속한 수렴결과를 확인하였다.

Keywords

References

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