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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 key point of numerical integration of gamma function to determine the relevant parameters of Pearson-Ⅲ curve lies in the calculation of the integral in the direction of horizontal coordinate, the core lies in the reasonable selection of steps to ensure the accuracy of calculation.In order to improve the calculation accuracy of numerical integration, Absolute error formula to determine the basic step function, derive a more perfect step-size integral function, using this function can quickly calculate the hydrological sequence corresponding to the Pearson-Ⅲ distribution under the frequency value of this method and social spider optimization Line method to estimate the hydrological frequency curve parameters of the general flood and extra-large flood sequences according to the minimum fitting criterion of lateral deviations and square deviation.Example verification results show that the Pearson-Ⅲ theoretical frequency curve obtained by this method is similar to the traditional Compared with the method of weight function, the moment method and the weight function method have better fitting results and higher accuracy than the empirical point method, which has great application value in hydraulic engineering design.