基于线性多步方法的二阶动力系统的模型识别  

Model Identification of Second-order Dynamical Systems Based on Linear Multistep Methods

作　　者：江月梅 陈浩 JIANG Yuemei;CHEN Hao(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《重庆工商大学学报（自然科学版）》2024年第6期80-86,共7页Journal of Chongqing Technology and Business University:Natural Science Edition

基　　金：重庆市自然科学基金(CSTC2021JCYJ-MSXMX0034)。

摘　　要：目的 针对二阶动力系统的识别问题,提出一种基于线性多步方法的稀疏识别方法。方法 首先,构造一个包含几乎所有可能基函数的基函数库,用于近似潜在的二阶动力系统;然后,利用线性多步方法离散近似后的二阶动力系统;接着,在广义最小二乘原理的指导下,选取一个合适的噪声残差项近似协方差矩阵,再利用该矩阵对上述过程得到的最小化问题进行加权,从而降低噪声对模型识别过程的影响;最后,使用稀疏回归算法从基函数库中挑选出最有意义的最小特征项,并通过稀疏迭代求解其对应系数。结果 比较了不同时间步长和不同噪声水平下,使用提出的线性多步稀疏识别方法挖掘潜在二阶动力系统的数值实验,通过这些实验可以得出:所提出的方法用于识别未知的二阶动力系统具有较高的精度和较好的鲁棒性。结论 通过数值实验,验证了算法的有效性。Objective A sparse identification method based on linear multistep methods was proposed for the identification of second-order dynamical systems.Methods Firstly,a basis function library containing nearly all possible basis functions was constructed to approximate the right-hand function of the potential second-order dynamical system.Then,the second-order dynamical system was discretized using linear multistep methods.Next,under the guidance of the generalized least squares principle,a suitable approximate covariance matrix of the noise residual term was selected and this matrix was used to weigh the minimization issues obtained by the above process to reduce the influence of noise on the model identification process.Finally,a sparse regression algorithm was used to select the most meaningful minimal feature terms from the basis function library and solve their corresponding coefficients through sparse iteration.Results Numerical experiments were done to explore potential second-order dynamical systems using the linear multistep sparse identification method with different time steps and noise levels.These experiments showed that the proposed method had higher accuracy and better robustness in identifying unknown second-order dynamical systems.Conclusion The effectiveness of the algorithm is verified by numerical experiments.

关 键 词：模型识别 线性多步法 稀疏回归 广义最小二乘法 

分 类 号：O241[理学—计算数学]