中文摘要：

针对输入输出均为连续时变函数的系统仿真问题，提出了一种基于函数基展开的神经网络建模方法．在连续函数空间中选择一组适当的基函数，将输入／输出函数在给定的拟合精度下，分别表示为该组基函数的有限项展开形式，由神经网络通过训练样本集的学习，建立输入函数基函数展开式系数与输出函数基函数展开式系数之间的变换关系．由于输入／输出函数与展开式系数之间存在着一一对应关系，从而可实现时变系统输入和输出之间的连续映射．给出了基于walsh变换的实现方法，并以油田开发驱替采油过程模拟为例验证了方法的有效性．

英文摘要：

Aiming at the problem of systems＇ simulation that input and output are all continuous time- varying functions, a new method of neural networks modeling which expands based on functions is proposed in this paper. A group of advisable basis functions is selected in continuous function space, and the input and output functions are respectively represented as the expansion form of limited basis functions within the specified precision. Neural networks constitute the conversion relationship between the expansion term coefficient of the basis function of input functions and output functions by learning the training samples. Because there is a one-to-one correlation between the input and output function and the expansion term coefficient, the insinuation relationship between the input and output of the continuous system can be carried out. The implementation methods based on Walsh conversion is given, and the effectiveness of this method is proved by tertiary oil recovery procedure simulation in oil field development.