基于采样稀疏学习的非线性动力系统辨识

Identification of Nonlinear Dynamical System Based on Sampling Sparse Learning

现有系统辨识方法常将非线性动力系统辨识问题转化为稀疏回归问题。针对现有方法应对噪声与小样本能力不足的问题,提出了一种基于采样稀疏学习的非线性动力系统辨识方法。首先,在复杂辨识问题被描述为稀疏回归问题的基础上,引入指示变量对稀疏结构进行编码;然后,基于嵌有Metropolis-Hastings算法的Gibbs采样器对稀疏结构进行学习;最后,通过简单的线性回归获得动力学方程的各项系数。实验结果表明,相较于LASSO算法,采样稀疏学习算法在较高的噪声水平下仍然保持较好的性能。此外,该算法无须进行阈值设定或正则化参数调整,具有更高的灵活性与鲁棒性。

Existing system identification approaches usually transform the identification of nonlinear dynamical system into a sparse regression problem.However,their performance may not be robust enough to noise and small sample size.To address this issue,a novel approach based on sampling sparse learning for identification of nonlinear dynamical system is proposed.Firstly,for the sparse regression problem derived from complex identification problem,indicator variables are introduced to encode sparse structures.Secondly,the sparse structure is learned by using the Gibbs sampler embedded with Metropolis-Hastings algorithm.Finally,the coefficients of the dynamical equation can be obtained by simple linear regression.The experimental results show that the sampling sparse learning algorithm still maintains better performance at high noise levels than LASSO algorithm.In addition,the proposed approach achieves sparse structures without threshold setting or regularization parameter fine-tuning,and therefore provides greater flexibility and robustness.