非线性自回归模型辨识及其在结构损伤识别中的应用

摘要

The similarities between the general expression for the linear and nonlinear auto-regressive model with exogenous inputs (GNARX) and Volterra series model,and the internal links between the GNARX and the autoregressive model with exogenous inputs (ARX) were analyzed.According to the structure characteristics of the GNARX model,a structure pruning algorithm based on parameters' rate of standard deviation was proposed and applied to model structure identification for the GNARX model.With simulation,the feasibility and effectiveness of the method was verified.Finally,the GNARX model together with the proposed structure identification method was applied to structural damage detection for a steel plate.The results show that the GNARX model,whose structure was identified with structure pruning algorithm based on parameters' rate of standard deviation,has the highest identification accuracy of structural damage.This indicates the superiority of the GNARX model and its structure pruning algorithm applied to structural damage detection.%分析了带有外部输入的线性/非线性自回归模型一般表达式(GNARX)与Volterra级数模型的相似之处,以及GNARX模型与带外部输入的自回归模型(ARX)之间的内在联系.根据GNARX模型结构特点,提出了一种基于参数离差率的结构剪枝算法,并用于模型结构辨识,通过数据仿真,验证了方法的可行性和有效性.最后,将GNARX模型结合提出的结构辨识方法,应用于钢板的损伤识别.结果显示,基于参数离差率的结构剪枝算法辨识GNARX模型结构,其损伤识别精度最高,体现了GNARX模型及其结构剪枝算法应用于结构损伤识别的优越性.