自适应差分进化算法在灌区频率分析中的应用

在较短水文系列下灌区规划设计水文频率分析中,枯水设计年的年径流量和年降雨量的精确度难以保证。差分进化算法具有收敛快、参数较少、较强的鲁棒性等特性,但标准差分进化算法具有搜索能力与开发能力相矛盾的缺点。【目的】引入一种随机扰动与三角函数相结合的迭代结构,保证迭代过程中变异随机性的同时加大收敛速率,构建可用于有较短水文系列的P-Ⅲ型分布曲线参数估值的自适应差分进化算法。【方法】以江西省赣州市南康区窑下坝站的实测降雨资料为例,分别选取1956—2010年和1981—2010年实测降雨量资料为长短系列降雨资料,计算长系列降雨资料下应用OLS准则的离差平方和及其在不同迭代次数下的标准差,计算长短系列降雨资料下不同枯水年的设计值,将自适应差分进化算法与遗传算法及传统的参数估计方法加以比较。【结果】自适应差分进化算法效率高、精度高、寻优结果稳定、鲁棒性强,在长短系列之间4个枯水年的设计值的误差之和最小。【结论】自适应差分进化算法适用于灌区规划的水文频率分析。

Analyzing Hydrological Frequency in Irrigation District Using Adaptive Differential Evolution Method

【Objective】Hydrological frequency analysis in planning and designing irrigation schedule for irrigation districts needs to dealt with short history of hydrological data, making the estimated annual runoff and rainfall in the design for dry years susceptible to uncertainty. The differential evolution method is simple and converges faster; it is also robust and needs less parameters, but with a conflict in search ability and potential for further development.【Method】This paper presents an iterative method by combining stochastic perturbation and trigonometric functions to ensure that the variation during the iteration was random in order to increase convergence. We constructed adaptive differential evolution algorithms in which a parameter estimation method can be used for the P-III distribution curve with short hydrology series. Taking the measured rainfall data from Yaoxiaba Station in Nankang District, Ganzhou City, Jiangxi Province as examples, rainfall measured in 55 years and 30 years were treated as long and short series respectively. Using the adaptive differential evolution algorithm, the genetic algorithm and the traditional parameter estimation method, the sum of squared deviation of the OLS and its standard deviation at different iterations for the long series of rainfall data for different dry years under the long and the short series were calculated and compared.【Result】The adaptive differential evolution algorithm was more efficient, accurate, robust, giving stable search results. For the long and short series, the adaptive differential evolution algorithm minimizes the sum of the errors in design for a period of four dry years.【Conclusion】The adaptive differential evolution algorithm is suitable for irrigation planning.