基于正交匹配追踪算法的复杂系统动力学建模与分析

Modelling and Analysis of Complex System Dynamics Based on Orthogonal Matching Pursuit Algorithm

针对非线性系统模型的辨识问题,通过引入正交匹配追踪(Orthogonal matching pursuit,OMP)算法实现快速非线性系统建模。该方法旨在解决非线性有源自回归(Nonlinear autoregressive with exogenous inputs,NARX)模型针对大型数据建模时效性差的问题。首先,说明了正交最小二乘(Orthogonal least squares,OLS)算法存在正交次数多、耗时长的问题,采用OMP算法可有效解决,通过与OLS算法对比正交差异性证明了OMP算法计算效率提升的理论基础,采用模型预报方法验证OMP算法所得NARX模型的动力学特性。其次,以单自由度非线性系统为例,说明了OMP算法系统建模的有效性。最后,利用OMP算法建立悬臂梁NARX模型,并分别将NARX模型预报输出与试验实测输出,NARX模型固有频率与悬臂梁实际固有频率进行对比。结果表明,与OLS算法相比,所提方法的建模效率平均提升了10倍,且模型可有效反应系统动力学特性。

The problem of identifying non-linear system models is addressed by introducing the OMP(Orthogonal matching pursuit)algorithm for fast non-linear system modelling. The method aims to solve the problem of poor timeliness in modelling large data with NARX(Nonlinear autoregressive with exogenous inputs) models. Firstly, it is shown that the OLS(Orthogonal least squares)algorithm has the problem of many orthogonal times and time consuming, which can be effectively solved by using the OMP algorithm. The kinetic properties of the NARX model obtained by the OMP algorithm are verified using the model prediction method.Secondly, the effectiveness of the OMP algorithm system modelling is illustrated by taking a single degree of freedom non-linear system as an example. Finally, the NARX model of the cantilever beam is established using the OMP algorithm, and the NARX model prediction output is compared with the experimental measured output, the inherent frequency of the NARX model and the actual inherent frequency of the cantilever beam respectively. The results show that the modelling efficiency of the proposed method is on average 10 times higher than that of the OLS algorithm, and the model can effectively reflect the dynamics of the system.