随机非线性系统辨识方法的关键技术研究

Because various phenomena existing in the physical and real world are non-linear in essence and the linearity is just some local approximation, in order to realize these phenomena it is more reasonable to use nonlinear models to describe them. This results in develping the algorithms for identifying nonlinear models. It is found that identifying some commonly used nonlinear systems can be attributed to two key technologies: variable selection and bias compensation by means of studying the existing algorithms for identifying these nonlinear systems. This is the focus of the project that is to study, where the variable selection technique is mainly used to explore the modeling of high-dimensional data by applying nonlinear models and bias compensation technique is mainly used to solve the problem under a unified framework that the linear least square is biased if the regressor and the noise is correlated. One expects to obtain some general apporaches to identifying some nonlinear systems by investigating the two key technologies in-depth and also expects that these approaches are applied to the closely related fields, e.g. the modeling and prediction of financial data, machine learning, data mining, signal denoising and so on.

因为现实世界存在的各种现象在本质上是非线性的，线性只是某种局部的近似，所以为了更好地认识这些现象使用非线性模型来描述这些现象更合理，这也促使辨识非线性模型的算法产生。通过研究一些已有的常见非线性系统的辨识算法发现解决这些非线性系统的辨识可以归结为两个关键技术：变量选择和偏差补偿，这也是本项目拟研究的重点，其中变量选择技术主要用于探索用非线性模型建模高维数据，而偏差补偿技术主要是在一个统一的框架下解决由回归向量与噪声的相关性导致线性最小二乘是有偏的这类问题。本项目希望通过对这两项关键技术的深入研究，得到辨识一些非线性系统的通用方法，也期望将其应用到与之密切相关的领域，比如，金融数据的建模和预测、机器学习、数据挖掘以及信号去噪等。

非线性系统广泛存在于自然科学和工程技术中，对其进行辨识是认识、控制和优化这些系统的有效方法。本项目研究了高维动态可加非线性系统的非参数辨识和变量选择、Hammerstein系统的递推辨识以及非线性有理系统的辨识，发展了适用于非线性系统辨识的变量选择和偏差补偿等关键技术，其中变量选择技术主要用于确定对系统输出真正有作用的输入变量，而偏差补偿技术则是解决已有方法的有偏性。通过对这两项关键技术的深入研究，得到了解决非线性系统辨识的有效方法。