为预测年径流这类高维复杂动力系统,提出了投影寻踪门限回归(PPTR)模型。构造了新的投影指标函数,用门限回归(TR)模型描述投影值与预测对象间的非线性关系,并用实码加速遗传算法优化投影指标函数和TR模型参数。实例的计算结果表明,用PPTR模型预测年径流是可行而有效的。PPTR模型简便、适用性强,克服了目前投影寻踪方法计算量大、编程实现困难的缺点,有利于投影寻踪方法的推广应用,为解决高维非线性复杂预测问题提供了新途径。

Today water resource is very important in the world. The variation of annual runoff not only influences economy and people's living standards, but also restricts the economic development. To solve these problems, accurately predicting the variation of annual runoff is indispensable to scientifically utilize water resources. Being the output of a rainfall-runoff system of drainage basin, the annual runoff time series is a very complex dynamic phenomenon varying from region to region and changing with time, which includes lots of past information of all variations and hides many laws. The evolution treads of annual runoff time series are often time irreversible, nonlinear with weak dependence. Now traditional methods for predicting annual runoff usually use linear technique, but the forecasting precision is not satisfactory, owing to complexity of its intrinsic evolutions, and its close and complicated relationships to climate change and other hydrologic effect factors. In order to predict the high dimension complex dynamic systems of the annual runoff system, a new model-projection pursuit threshold regressive (PPTR) model is presented in this paper. A scheme of PPTR modeling is also given to reduce the computational amount, a new function of projection indexes is constructed, the relation of projection value and predicted object can be described with threshold regressive (TR) model, and it is suggested that both the function of projection indexes and the parameters of TR model can be optimized by using a real coded genetic algorithm developed by the authors. The examples of predicting annual runoff show that PPTR model is both practical and effective. PPTR model is simple and general, which overcomes the shortcomings of large amount of computation and difficulty of computer programming in traditional projection pursuit methods, benefits the more applications of projection pursuit, and gives a new approach to resolving the high dimension, nonlinear complex predictive problems.