基于群居蜘蛛优化算法的自适应数值积分皮尔逊-Ⅲ型曲线参数估计

The Adaptive Numerical Integral Pearson-Ⅲ Curve Parameters Estimation Based on SSO

伽马函数数值积分确定皮尔逊-Ⅲ型曲线的相关参数,关键在于横向坐标方向上积分的计算,核心在于合理选择步长以保证计算精度.为了能够更好地提高数值积分的计算精度,利用绝对误差公式确定基本步长函数,推导了较为完善的变步长积分函数,采用该函数能够快速计算出水文序列在皮尔逊-Ⅲ型分布下所对应的频率值.该方法和群居蜘蛛优化适线法相结合,依据横向离差平方和最小的适线准则,用于估计一般洪水和特大洪水序列的水文频率曲线参数.实例验证结果表明:该方法得到的皮尔逊-Ⅲ型理论频率曲线与传统的矩法和权函数法相比对经验点据拟合效果较好,精度较高,在水利工程设计中有较大的应用价值.

The related parameters of Pearson Ⅲ type curve are determined by Gamma function numerical integration,and its key lies in transverse direction integral calculation,core lies in the choice of reasonable step to ensure the calculation accuracy. In order to better improve the calculation accuracy,the absolute error formula is used to make the basic step function and to deduce the function of relatively perfect integral. The hydrological sequence under the Pearson-Ⅲ type distribution of the frequency values can be quickly calculated with the function.According to the transverse deviation minimum sum of squares of optimum criterion,the method associated with the optimum line of social spider optimization method was used to estimate the general flood and hydrologic frequency curve parameters of the flooding sequence. The results of example shows that the obtained Pearson-Ⅲ theoretical frequency curve is better fitting effect and high precision with experience points,which is compared with the traditional moment method and the weight function method. Therefore,it has great practical value in water conservancy engineering design.