基于非理想数据的模块化非线性系统偏差校正多重正则子空间辨识方法研究

The existing nonlinear system identification methods may fail to get model estimates with good accuracy and robustness for complex multivariable time-varying nonlinear systems from nonideal data records, where nonideal means that the number of data records is short, the signal-to-noise ratio is low, or both the input and output are contaminated by noise (also called errors-in-variables, EIV). In this project, the bias-correction and multi-regularization based subspace identification methods will be studied to deal with the above-mentioned nonideal data records, which are able to provide accuracy and robust block-oriented state-space nonlinear models. Three main research contents are considered in this project, namely: (1) For block-oriented identification of errors-in-variables nonlinear systems, develop several bias-correction identification algorithms to guarantee the consistency of the nonlinear model extended parameter estimates based on the use of higher order cumulate statistics; (2) To handle the scenarios when the data record is short or the signal-to-noise ratio is low, the multiple-regularization identification algorithms will be studied by developing the variational method in combination with alternating direction multiplier method based on the hierarchical identification principle, so as to guarantee the accuracy and robust estimates for identifying block-oriented nonlinear models; (3) The recursive bias-correction and multiple-regularization identification algorithms to deal with the above-mentioned nonideal data records, which are the extensions of the above-mentioned algorithms for complex multivariable time-varying nonlinear systems. The research outcomes of this project will provide the modeling theory foundation for identifying complex nonlinear systems from nonideal data records, and have practical reference value and application merits to improve the model-based control technology level for industrial processes.

在有限低信噪比输入输出受白噪声影响数据（非理想数据）情况下，现有非线性系统辨识方法难以实现对复杂多变量耦合时变非线性系统的精确鲁棒辨识。为此，项目拟研究面向非理想数据复杂非线性系统模块化状态空间模型精确鲁棒辨识的偏差校正多重正则子空间辨识方法。项目将开展以下研究：（1）针对难以消除非线性系统输入噪声影响的问题，研究基于平稳随机过程高阶矩理论的偏差校正消噪辨识方法，实现对模型扩展参数的一致估计；（2）针对难以处理非线性系统有限低信噪比数据的问题，研究基于递阶变分法和交替方向乘子法的多重正则辨识算法，实现对模型参数和阶次的精确鲁棒辨识；（3）针对难以在线处理非线性系统非理想数据的问题，研究递归偏差校正多重正则辨识方法，实现对多变量耦合时变非线性系统模型的精确辨识。项目将为基于非理想数据的复杂非线性系统精确鲁棒辨识提供理论基础，对提高工业过程基于模型的控制技术水平具有实际参考和应用价值。

在有限低信噪比输入输出受白噪声影响数据（非理想数据）情况下，现有非线性系统辨识方法难以实现对复杂多变量耦合时变非线性系统的精确鲁棒辨识。为此，项目研究面向非理想数据复杂非线性系统模块化状态空间模型精确鲁棒辨识的偏差校正多重正则子空间辨识方法。项目主要研究内容和成果为：1）针对难以消除非线性系统输入白噪声影响的问题，首先探明现有子空间辨识方法在输入输出受白噪声影响非线性系统辨识中产生偏差的内在原因并且确定估计误差，提出了偏差校正子空间辨识方法以消除估计误差获得无偏估计参数；证明算法实现无偏估计的充分条件。2）针对难以处理非线性系统有限低信噪比数据的问题，研究基于递阶变分和交替方向乘子的辨识算法，实现对模型参数和阶次的精确鲁棒辨识；3）针对难以在线处理非线性系统非理想数据的问题，研究递归偏差校正多重正则遗忘因子加权最小二乘辨识方法，实现对多变量耦合时变非线性系统模型的精确辨识。项目将为基于非理想数据的复杂非线性系统精确鲁棒辨识提供理论基础，为基于模型的控制系统设计和性能优化提供精确有效的数学模型，有力促进非线性系统基于模型的控制理论和工程运用，促进系统辨识学科由理论研究走向实际运用，对提高工业过程基于模型的控制技术水平具有实际参考和应用价值。依托项目共获得成果16项，具体为发表期刊论文12篇、会议论文1篇，获得授权国家发明专利1项、获得重庆市科技进步一等奖奖励1项、川渝科技学术大会优秀论文1篇。所发表期刊论文含6篇中科院1区Top期刊论文如IEEE-TIE/IEEE-SMCA/IEEE-TPE等、2篇中科院2区期刊论文如JPC/CACE等、2篇中科院3区期刊论文、北大中文核心中文论文2篇，其中含自动化学会等一级学会推荐高水平期刊6篇，川渝科技大会优秀论文1篇。