NARMAX模型辨识的直交化最小二乘新算法

基于实际中常用的ＣＧＳ（ＣｌａｓｓｉｃａｌＧｒａｍ－Ｓｃｈｍｉｄｔ）、ＭＧＳ（ＭｏｄｉｆｉｅｄＧｒａｍ－Ｓｃｈｍｉｄｔ）、ＨＴ（ＨｏｕｓｅｈｏｌｄｅｒＴｒａｎｓｆｏｒｍａｔｉｏｎ）及Ｇｉｖｅｎｓ算法，给出了１类改进的直交化最小二乘新算法，分别称之为改进的ＣＧＳ、ＭＧＳ、ＭＨＴ及ＭＧＶ算法，改善了原算法的数值稳定性．将改进算法用于非线性ＮＡＲＭＡＸ模型辨识，构造出了１种新的模型结构与参数辨识的一体化算法．新算法基于逐步回归进行模型选项并消去模型中的冗余项，保证了最终模型的结构优化，并可给出比Ｂｉｌｉｎｇｓ等算法精度更高的参数估计．仿真结果证明了文章中算法的优越性

New Modified Orthogonal Least Squares Algorithms for NARMAX Model Identification

Based on the CGS (Classical Gram Schmidt), MGS(Modified Gram Schmidt), HT(Householder Transformation) and Givens algorithms, a new kind of modified orthogonal least squares algorithms referred to as the MCGS(Modified on CGS), MMGS(Modified on MGS), MHT(Modified on Householder Transformation) and MGV(Modified on Givens) algorithms are proposed in this paper, which are numerical superior to the original ones. Applied them for the NARMAX model identification, a new integrated algorithm of structure determination and parameter estimation has been proposed here. It selects the model terms by stepwise regression procedure, giving the optimal model structure without unnecessary terms involved and a higher accuracy for the parameter estimation compared with the CGS algorithm proposed by Billings. The simulation results indicate their superiority.