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Parameter estimation method based on parameter function surface

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Abstract

By analyzing the structure of the objective function based on error sum of squares and the information provided by the objective function, the essential problems in the current parameter estimation methods are summarized: (1) the information extracted from the objective function based on error sum of squares is unreasonable or even wrong for parameter estimation; and (2) the surface of the objective function based on error sum of squares is more complex than that of the parameter function, which indicates that the optimal parameter values should be searched on the surface of the parameter function instead of the objective function. This paper proposes the concept of sample intersection and demonstrates the uniqueness theorem of intersection point (namely the uniqueness of optimal parameter values). According to the characteristics of parameter function surface and Taylor series expansion, a parameter estimation method based on the sample intersection information extracted from parameter function surface (PFS method) was constructed. The results of theoretical analysis and practical application show that the proposed PFS method can avoid the problems in the current automatic parameter calibration, and has fast convergence rate and good performance in parameter calibration.

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References

  1. Burke J V, Ferris M C. A Gauss-Newton method for convex composite optimization. Math Program, 1995, 71: 179–194

    MathSciNet  MATH  Google Scholar 

  2. Rosenbrock H H. An automatic method of finding the greatest of least value of a Function. The Comp J, 1960, 3: 303–307

    MathSciNet  Google Scholar 

  3. Powell M J D. An efficient method for finding the minimum of a function of several variables without calculating derivatives. The Comp J, 1964, 7: 155–162

    Article  MATH  Google Scholar 

  4. Pickup G. Testing the efficiency of algorithms and strategies for automatic calibration of rainfall-runoff models. Hydrol Sci Bull, 1977, 22(2–6): 257–274

    Google Scholar 

  5. Sorooshian S, Brazil E L. Comparison of Newton-type and direct search algorithms for calibration of conceptual rainfall-runoff models. Water Resour Res, 1988, 24(5): 691–700

    Article  Google Scholar 

  6. Hofmann B. On the degree of ill-posedness for nonlinear problems. J Inverse III-posed Prob, 1994, 2(1): 61–76

    MATH  Google Scholar 

  7. Hofmann B, Scherzer O. Factors influencing the ill-posedness of nonlinear problems. Inverse Probl, 1994, 10(6): 1277–1297

    Article  MathSciNet  MATH  Google Scholar 

  8. Beven K. A manifesto for the equifinality thesis. J Hydrol, 2006, 320(1–2): 18–36

    Article  Google Scholar 

  9. Hooke R, Jeeves T A. Direct search solutions of numerical and statistical problems. J ACM, 1961, 8(2): 212–229

    Article  MATH  Google Scholar 

  10. Ibbitt R P, Donnell T O’. Designing conceptual catchment models for automatic fitting methods. In: Proceedings of International Symposium on Mathematical Models in Hydrology, International Association of Hydrological Science, Warsaw, 1971

    Google Scholar 

  11. Francine M. Using a genetic algorithm combined with a local search method for the automatic calibration of conceptual rainfall-runoff models. Hydrolog Sci J, 1996, 41(1): 21–40

    Article  Google Scholar 

  12. Cheng C T, Wang W C, Xu D M, et al. Optimizing hydropower reservoir operation using hybrid genetic algorithm and chaos. Water Resour Manag, 2008, 22(7): 895–909

    Article  Google Scholar 

  13. Blum C. Ant colony optimization: Introduction and recent trends. Phys Life Rev, 2005, 2(4): 353–373

    Article  Google Scholar 

  14. Yang J G, Zhuang Y B. An improved ant colony optimization algorithm for solving a complex combinatorial optimization problem. Appl Soft Comput, 2010, 10(2): 653–660

    Article  Google Scholar 

  15. Chau K W. Particle swarm optimization training algorithm for ANNs in stage prediction of Shing Mun River. J Hydrol, 2006, 329(3–4): 363–367

    Article  Google Scholar 

  16. Jiang Y, Liu C M, Huang C C, et al. Improved particle swarm algorithm for hydrological parameter optimization. Appl Math Comput, 2010, 217: 3207–3215

    Article  MathSciNet  MATH  Google Scholar 

  17. Hopfield J, Tank D. ‘Neural’ computation of derisions in optimization problems. Biologieal Cyberneties, 1985, 52: 141–152

    MathSciNet  MATH  Google Scholar 

  18. Duan Q Y, Sorooshian S, Gupta V. Effective and efficient global optimization for conceptual rainfall-runoff models. Water Resour Res, 1992, 28(4): 1015–1031

    Article  Google Scholar 

  19. Duan Q Y, Gupta V K, Sorooshina S. Shuffled complex evolution approach for effective and efficient global minimization. J Optimiz Theory App, 1993, 76(3): 501–521

    Article  MATH  Google Scholar 

  20. Gupta H V, Sorooshian S, Yapo P O. Status of automatic calibration for hydrologic models: comparison with multilevel expert calibration. J Hydrol Eng, 1999, 4 (2): 135–143

    Article  Google Scholar 

  21. Franchini M, Galeati G. Comparing several genetic algorithm schemes for the calibration of conceptual rainfall-runoff models. Hydrolog Sci J, 1997, 42 (3): 357–379

    Article  Google Scholar 

  22. Goswami M, O’Connor K M. Comparative assessment of six automatic optimization techniques for calibration of a conceptual rainfall-runoff model. Hydrolog Sci J, 2007, 52(3): 432–449

    Article  Google Scholar 

  23. Xia Y, Pitman H V, Gupta M, et al. Calibrating a land surface models of varying complexity using multi-objective methods and the Cabauw data set. J Hydrometeorol, 2002, 3:181–194

    Article  Google Scholar 

  24. Engeland K, Braud I, Gottschalk L, et al. Multi-objective regional modeling. J Hydrol, 2006, 327(3–4): 339–351

    Article  Google Scholar 

  25. Gupta H V, Sorooshian S, Yapo P O. Toward improved calibration of hydrologic models: Multiple and noncommensurable measures of information. Water Resou Res, 1998, 34(4): 751–763

    Article  Google Scholar 

  26. Bao W M. The research about calibrating model parameters (in Chinese). Doctoral Dissertation. Nanjing: Hohai Univ, 1989

    Google Scholar 

  27. Bao W M. Automatic calibration of the Xinanjiang model (in Chinese). J Hohai Univ (Natural Sci.), 1986, (4): 22–30

    Google Scholar 

  28. Li Q, Bao W M, Zhang B, et al. Conceptual hierarchical calibration of Xinanjiang model. 3rd International Symposium on Methodology in Hydrology, IAHS Publ 350, 2011. 690–697

    Google Scholar 

  29. Bao W M. Parameter estimation of the model with colored noise (in Chinese). J Hydraul Eng, 1991, (12): 47–52

    Google Scholar 

  30. Bao W M, Ji H X, Hu Q M, et al. Robust estimation theory and its application to hydrology (in Chinese). Adv Water Sci, 2003, 14(4): 133–137

    Google Scholar 

  31. Bao W M, Lin Y, Huang X Q, et al. Parameter robust estimation of reach flood concentration model (in Chinese). Eng J Wuhan Univ, 2004, 37(6): 13–17

    Google Scholar 

  32. Zhao C, Bao W M, Wang Y Q, et al. Robust estimation of reach flow concentration parameters (in Chinese). J Hohai Univ (Nature Sci), 2006, 34(1): 14–17

    Google Scholar 

  33. Bao W M, Wang H, Zhao C, et al. Robust estimation of AR model parameters (in Chinese). J Hohai Univ (Nature Sci), 2006, 34(3): 258–261

    Google Scholar 

  34. Zhao C, Hong H S, Bao W M, et al. Robust recursive estimation of auto-regressive updating model parameters for real-time flood forecasting. J Hydrol, 2008, 349(3–4): 376–382

    Google Scholar 

  35. Bao W M, Li Q. Estimating selected parameters for the XAJ model under multicollinearity among watershed characteristics. J Hydrol Eng, 2012, 17(1): 118–128

    Article  Google Scholar 

  36. Bao W M, Li Q, Li C S. The weighed objective functions based on sensitivity analysis (in Chinese). J Hydroelectric Eng, 2013 (accepted)

    Google Scholar 

  37. Li Q, Bao W M. The estimation of concentration parameters based on the Fourier (in Chinese). Water Resour power, 2011, 2: 33–38

    Google Scholar 

  38. Bao W M, Si W, Qu S M. The linearized calibration method of non-linear function parameter (in Chinese). Chin J Comp Mech, 2013, 30(2): 236–241

    Google Scholar 

  39. Bao W M, Li Q. An efficient calibration technique under the irregularity response surface. J Hydrol Eng, 2013, http://dx.doi.org/10.1061/(ASCE)AE.1943-5584.0000719

    Google Scholar 

  40. Nelde J A, Mead R. A simplex method for function minimization. The Computer J, 1965, (7): 308–313

    Google Scholar 

  41. Zhao R J. The Xinanjiang model applied in China. J Hydrol, 1992, 135(4): 371–381

    Google Scholar 

  42. Yao C, Li Z J, Bao H J. Application of a developed Grid-Xinanjiang model to Chinese watersheds for flood forecasting purpose. J Hydrol Eng, 2009, 14(9): 923–934

    Article  Google Scholar 

  43. Hu C H, Guo S L, Xiong L H. A modified Xinanjiang model and its application in northern China. Nordic Hydrol, 2005, 36(2): 175–192

    Google Scholar 

  44. Cheng C T, Zhao M Y, Chau K W. Using genetic algorithm and TOPSIS for Xinanjiang model calibration with a single procedure. J Hydrol, 2006, 316(1–4): 129–140

    Article  Google Scholar 

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Authors and Affiliations

  1. State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing, 210098, China

    WeiMin Bao, XiaoQin Zhang & LiPing Zhao

  2. College of Hydrology and Water Resources, Hohai University, Nanjing, 210098, China

    WeiMin Bao, XiaoQin Zhang & LiPing Zhao

Authors
  1. WeiMin Bao
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  2. XiaoQin Zhang
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  3. LiPing Zhao
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Correspondence to XiaoQin Zhang.

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Bao, W., Zhang, X. & Zhao, L. Parameter estimation method based on parameter function surface. Sci. China Technol. Sci. 56, 1485–1498 (2013). https://doi.org/10.1007/s11431-013-5224-3

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  • DOI: https://doi.org/10.1007/s11431-013-5224-3

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