模糊加权优化适线法的改进及统计特征分析

Improvement and Statistical Performance of Fuzzy Weighted Optimum Curve-fitting Method

水文序列长度有限,频率曲线参数估计存在抽样误差,采用加权适线法能够很好地减小误差。模糊加权优化适线法的诺模图长度有限,而且隶属度函数不是以样本无穷大为前提,对模糊加权优化适线法改进,提出半降正态分布的隶属度函数,运用大样本统计试验方法延长诺模图。以理想数据、蒙特卡洛随机数和实测序列对改进的方法检验,以无偏性和有效性为评价指标,运用评分法和百分率法对统计结果分析评价。结果表明改进的模糊加权优化适线法的统计特性好,适线精度高,能够促进模糊加权优化适线法在实际工程中的推广应用。

Hydrological sequence length is limited, so that frequency curve parameter estimate of sampling exists error which can be effectively reducedby weighted optimum line method.Normograph length of weighted fuzzy optimization optimal line method is limited, and the membership function is not on the base of the infinite sample. The fuzzy weighted optimization optimal line method was improved by proposing half normal distribution of membership functions and using large sample statistical test method for extension of normograph. The ideal data, Monte Carlo random number and the practical sequence were used to test with umbiasedness and efficiency as evaluation index by using the method of grading method and the percentage of statistic analysis for the evaluation.The resultshows that the improved fuzzy weighted optimization optimal line has good statistical properties, high precision of optimum line. Andthe improved method can promote the fuzzy weighted optimization optimal line method to be applied in practical engineering.