自回归模型和基于数据处理分组法的非线性模型的比较研究

The Comparison Research of AR Model And Non-linear Model Based on GMDH

为信号建立非线性模型，既是非线性动力学（例如混沌理论）研究中关心的课题，也是信号处理及系统辨识的核心课题之一。由于实际生物系统总是有非线性的，因此建立非线性模型比线性模型更具普遍意义。数据处理的群集算法（ＧｒｏｕｐＭｅｔｈｏｄｏｆＤａｔａＨａｎｄｌｉｎｇ，ＧＭＤＨ）是根据给定数据建立非线性模型的有效方法。作者吸收人工神经网络中反传算法的思想，把ＧＭＤＨ算法进一步发展成自适应算法，使之可以随着数据的不断输入自动调整参数，以跟随数据统计特性的变化。作者还以心电数据为例进行了处理，结果证明其性能确实比线性的ＡＲ模型更优。

The construction of non-linear models of signals is not only concerned tasks in non-linear dynamical(eg. chaotic theory)research ,but also one of the major tasks in signal processing and system identification. As there is always some non-linearity in real biological systems,the non-linear models are even of more importance than linear ones.The GMDH(Group Method of Data Handling)algorithm is an efficient method to construct the non-linear model with given data. But the method is used mainly for block data processing,so it can't be used adaptively. In this paper the idea of Back-propagation of Artificial Neural Network is adopted and then the GMDH algorithm is further developed to be an adaptive one. This makes it possible to auto-adjust the model's parameters of the system according to the successive input data ,and also to follow the variation of the statistical behavior of the data. The results of the handling of ECG data show that its performance is better than that of the linear AR model.