一类变量带误差系统辨识的新方法及其应用

The proposal deals with estimation of transmissibility function for the purpose of modeling dynamical systems excited by arbitrary unknown excitations. Considering the fact that the system responses used for transmissibility estimation are random and unknown (due to ambient perturbations), and both contaminated by possibly correlated noises, a novel Errors-in-Variables (EIV) identification method is proposed for dynamical systems. Nonparametric estimation is firstly established to properly determine the orders of the plant model and of the input-output noise models. The parametric identification methodology is developed for the plant model and the noise model by proposing a key strategy of constructing the cost function, the identifiability of the system is also addressed. Regarding the difficulty in identifying the EIV system involving the colored disturbing noise and high-order plant model, an efficient nonparametric-parametric identification strategy is implemented. The statistical accuracy of the estimator is further evaluated, its robustness in the presence of the modeling error is considered as well. Finally, the application of the proposed method on the estimation of transmissibility functions is experimentally validated in the laboratory, and tested in the real life ambient environment. By carrying out the current research proposal, a methodology is developed for the accuracy estimation of the transmissibility function, which is fundamental for the identification and health monitoring of large-scale structures (e.g., flight and wind turbine) operating in their working conditions.

本课题围绕任意未知随机输入条件下系统建模的科学问题，开展系统输出信号之间传递率函数模型的辨识研究。针对用于传递率函数估计的响应信号由于受外部激励干扰而具有任意性和未知性、以及含有互相关扰动噪声的问题，提出一类变量带误差系统辨识的新方法。建立变量带误差系统的非参数辨识方法，正确界定系统及扰动噪声模型的阶次；提出成本函数构造的关键策略，发展变量带误差系统的参数辨识新理论，阐明系统满足可辨识性的充分条件，建立模型参数的非参数-参数估计策略；评价参数估计的统计精度以及模型误差存在情形下的鲁棒性。最后，基于所建立的系统辨识方法开展室内环境下传递率函数估计的实验验证以及外场环境下的实际应用。通过本项目的开展，将建立一套传递率函数的高精度估计方法，为处于运行状态的飞行器、风电叶片等大型结构的参数辨识和健康监测奠定理论基础。

变量带误差系统辨识旨在从含有噪声的输入和输出数据中获取系统模型，揭示真实输入与真实输出之间的内在联系，广泛应用在控制、机械、通信、经济、生化等领域。 本工作率先开展了任意平稳随机输入条件下变量带误差系统辨识的基础性工作，针对单/多变量动态系统、互/不相关输入输出量测白噪声等情形，在辨识框架的构造、系统可辨识性、估计量的渐近性质、参数优化算法、精度分析等方面进行了较为深入的研究，主要结果如下：..（1）系统可辨识性证明。针对非最小相位系统、互相关输入输出量测白噪声及非参数真实输入，提出了基于雅可比梯度矩阵满秩的可辨识性准则，构造了变量带误差系统满足可辨识性的充分条件。.（2）变量带误差系统参数辨识。针对量测白噪声情形，提出了一类频率似然辨识方法，它超越了经典极大似然辨识框架，便可实现强一致估计，且系统模型参数的估计不确定度随着信噪比的提高逼近Cramér-Rao不等式下边界。.（3）变量带误差系统非参数辨识。针对随机输入信号，扩展局部多项式方法至变量带误差框架，不需要输入输出量测白噪声之间的方差比值，也不需系统模型的阶次，实现了非参数传递函数和噪声方差的一致估计。..这些研究成果初步形成了量测白噪声情形下的广义极大似然辨识方法，丰富了现有系统辨识理论与方法体系。本工作得到了系统辨识领域国内外研究学者的高度认可，在本领域国际顶级期刊Automatica发表了2篇学术论文。