考虑经验因素的暴雨频率曲线最优化拟合算法
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TU992.02

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国家自然科学基金(51608242);云南省人才培养计划(14118943)


Optimal fitting algorithm of rainstorm frequency curve considering the empirical factors
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    摘要:

    暴雨频率曲线拟合是推求暴雨强度公式必不可少的步骤,考虑经验因素进行暴雨频率曲线拟合,提出将暴雨强度频率曲线拟合作为最优化问题,采用加权阻尼高斯牛顿迭代算法求解。与已有方法相比,提出引入权重系数以提高工程常用重现期段拟合精度,避免不同历时暴雨频率曲线相交;提出应用有限差分法简化雅克比矩阵计算,并在海塞矩阵对角添加阻尼系数改进迭代收敛。以云南省保山市隆阳区33 a实测降雨资料为例,证明了算法的可行性及实用性。

    Abstract:

    The rainstorm frequency curve fitting is essential for the identification of storm intensity formula, the study of rainstorm frequency curve fitting with considering of experience factors was carried out, and put forward to regard the rainstorm intensity frequency curve fitting as an optimization problem, and then to solve it by the weighted damped Gauss-Newton iterative algorithm. Compared to existing methods, the proposed method introduced weight coefficients to improve the fitting precision of commonly used recurrence period in engineering, and to avoid the intersection problem of different frequency curves. The finite difference method is proposed to simplify the calculation of Jacobian matrix, and the damping coefficient was added in Hesse matrix to improve iterative convergence. Thirty-three years of rainfall data of Longyang District of Baoshan city in Yunnan Province were used as an example to illustrate and demonstrate the feasibility and practicability of the proposed algorithm.

    参考文献
    [1] 车伍, 杨正, 赵杨,等. 中国城市内涝防治与大小排水系统分析[J]. 中国给水排水, 2013, 29(16):13-19. CHE W, YANG Z, ZHAO Y, et al. Analysis of urban flooding control and major and minor drainage systems in China[J]. China Water & Wastewater, 2013, 29(16):13-19. (in Chinese)
    [2] CHE G W. Pearson-Ⅲ frequency curve plotting in Excel table[J]. Applied Mechanics & Materials, 2014, 556-562:5829-5834.
    [3] 王正发. MATLAB在P-Ⅲ型分布离均系数ϕp值计算及频率适线中的应用[J]. 西北水电, 2007(4):1-4. WANG Z F. MATLAB programming language used to calculate variation coefficient ϕp of the P-Ⅲ distribution and fit a frequency curve[J]. Northwest Hydropower, 2007(4):1-4. (in Chinese)
    [4] BLAIN G C. Standardized precipitation index based on pearson type Ⅲ distribution[J]. Revista Brasileira De Meteorologia, 2014, 26(2):167-180.
    [5] 崔俊蕊, 王政然, 梁爽,等. 城市设计暴雨频率曲线的拟合及参数优化[J]. 水电能源科学, 2014(11):48-51. CUI J R, WANG Z R, LIANG S, et al. Fitting and parameter optimization of urban design storm frequency curve[J]. Water Resources and Power, 2014(11):48-51. (in Chinese)
    [6] MANDAL K G, PADHI J, KUMAR A, et al. Analyses of rainfall using probability distribution and Markov chain models for crop planning in Daspalla region in Odisha, India[J]. Theoretical and Applied Climatology, 2015, 121(3):517-528.
    [7] WU Y C, LIU J J, SU Y F, et al. Establishing acceptance regions for L-moments based goodness-of-fit tests for the Pearson type Ⅲ distribution[J]. Stochastic Environmental Research and Risk Assessment, 2014, 26(6):873-885.
    [8] 高琳, 周玉文, 唐颖, 等. 城市暴雨强度公式皮尔逊Ⅲ型适线问题研究[J]. 给水排水, 2016(8):47-51. GAO L, ZHOU W Y, TANG Y, et al. Research on the fitting of pearson type Ⅲ in urban storm water intensity equation[J]. Water & Wastewater Engineering, 2016(8):47-51. (in Chinese)
    [9] RAFIQ A, RAFIULLAH M. Some multi-step iterative methods for solving nonlinear equations[J]. Computers & Mathematics with Applications, 2009, 58(8):1589-1597.
    [10] FAIRBANK M, ALONSO E. Efficient calculation of the Gauss-Newton approximation of the Hessian matrix in neural networks[J]. Neural Computation, 2012, 24(3):607-610.
    [11] ZHANG J, GENG X, DAI R. Analysis on two approaches for high order accuracy finite difference computation[J]. Applied Mathematics Letters, 2012, 25(12):2081-2085.
    [12] HAN Q, ZHANG Q S. An upper bound for hessian matrices of positive solutions of heat equations[J]. The Journal of Geometric Analysis, 2016, 26(2):715-749.
    [13] ERINA M Y,IZMAILOV A F. The Gauss-Newton method for finding singular solutions of systems of nonlinear equations[J]. Anz Journal of Surgery, 2015, 58(2):395-405.
    [14] PHAN A H, TICHAVSKY P, CICHOCKI A. Low complexity damped Gauss-Newton algorithms for CANDECOMP/PARAFAC[J]. Siam Journal on Matrix Analysis& Applications, 2013, 34(1):126-147.
    [15] SHEHU Y. Iterative method for fixed point problem, variational inequality and generalized mixed equilibrium problems with applications[J]. Journal of Global Optimization, 2013, 52(1):57-77.
    [16] JIN Q. Further convergence results on the general iteratively regularized Gauss-Newton methods under the discrepancy principle[J]. Mathematics of Computation, 2013, 82(283):1647-1665.
    [17] MACIEL L, GOMIDE F, BALLINI R. A differential evolution algorithm for yield curve estimation[J]. Mathematics & Computers in Simulation, 2016, 129:10-30.
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姬鹏杰,杜坤,冯燕,周明,杜雨.考虑经验因素的暴雨频率曲线最优化拟合算法[J].土木与环境工程学报(中英文),2018,40(2):77-82. Ji Pengjie, Du Kun, Feng Yan, Zhou Ming, Du Yu. Optimal fitting algorithm of rainstorm frequency curve considering the empirical factors[J]. JOURNAL OF CIVIL AND ENVIRONMENTAL ENGINEERING,2018,40(2):77-82.10.11835/j. issn.1674-4764.2018.02.012

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  • 收稿日期:2017-03-14
  • 在线发布日期: 2018-03-08
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