【摘要】 主曲线是用一维光滑曲线对数据集合进行信息抽取的一种方法,是第一主成分的非线性推广。通过分析传统回归方法在水轮机特性曲线数值拟合中存在的问题,提出了利用主曲线作为数学工具对水轮机特性曲线进行数值拟合。理论分析与实践表明,利用主曲线方法进行水轮机特性曲线的数值拟合,不仅拟合精度可以得到保证,而且对各种曲线可以用以投影指标为自变量的统一的数学表达式进行描述。该方法为水轮机特性曲线的数值拟合提供了一个新途径。更多还原

【Abstract】 Principal curve is a method of using one dimension smooth curve to finish information extract of a data set and can be regarded as the nonlinear generalization of the first principal component. The method of using principal curve as a mathematical tool is proposed by analyzing the problem of conventional regression analysis in numerical simulation of characteristic curves of hydraulic turbine. The results of theory analysis and practice show that numerical simulation of characteristic curves of hydraulic turbine by using the method of principal curves not only ensure the accurate simulation but also can give the mathematical expression which can be described by independent variable of projection index. This method provides a new way for numerical simulation of characteristic curves of hydraulic turbine.更多还原