一种线性/非线性自回归模型及其在建模和预测中的应用  

A linear and nonlinear auto-regressive model and its application in modeling and forecasting

作　　者：马家欣[1] 许飞云[1] 黄仁[1] 

机构地区：[1]东南大学机械工程学院,南京211189

出　　处：《东南大学学报（自然科学版）》2013年第3期509-514,共6页Journal of Southeast University：Natural Science Edition

基　　金：国家自然科学基金资助项目(51175079)

摘　　要：为提高模型准确性,在经典时序建模策略的基础上,提出了一种带有外部输入的线性/非线性自回归模型,并应用Weierstrass逼近定理推导出其一般表达式(GNARX),该模型允许带有多个外部输入以实现复杂系统的建模和辨识.针对该模型结构给出了其最小二乘参数估计方法,并采用结合建模误差、预测误差及模型复杂度的修正信息准则(AIC)确定最优模型结构.最后,将该模型应用于仿真数据和振动位移采样电流数据的建模与预测.结果表明,GNARX模型的建模和预测精度均高于AR,GNAR,ARX模型及BP神经网络模型,表现出良好的线性/非线性建模和预测能力,及较好的通用性和实用价值.To improve the model accuracy,a linear and nonlinear auto-regressive model with exogenous inputs is proposed based on classical time series modeling strategy.And,with the Weierstrass approximation theorem,the general expression for the linear and nonlinear auto-regressive model with exogenous inputs（GNARX） is deduced.As multiple exogenous inputs are allowable,this model can realize modeling and identification of complex systems.Furthermore,concerning the model structure,a least square parameter estimation method is presented.With modified information criterion（AIC） integrated with modeling error,forecasting error and model complexity,the optimal model is determined.Finally,this model is applied to the modeling and forecasting of simulation data and the current sampling data of vibration displacement.The results show that the modeling and forecasting accuracy of the GNARX model is higher than those of AR,GNAR,ARX models and BP neural network,indicating that the GNARX model has good linear and nonlinear modeling ability and forecasting ability with good universality and practical value.

关 键 词：线性 非线性自回归模型 建模 预测 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]