带稀疏特性的最优区间回归模型辨识方法

A Method for Identifying Optimal Interval Regression Model with Sparsity

传统的系统辨识方法主要是针对确定性数学模型辨识,其输出为确定的点输出,鲁棒性差,易受外界干扰。本文针对此问题,提出了最优区间回归模型(OIRM)辨识的方法。该方法将逼近误差的?1范数思想与结构风险最小化理论相结合,建立求解区间模型的最优化问题,应用线性规划独立求解区间模型的上界和下界模型。实验分析表明,对来自测量以及参数不确定性的数据,从均方根误差(RMSE)以及支持向量的百分数(SVs%)两个指标论证了,提出的方法不仅可以获取最优区间输出,还能确定区间模型的辨识精度和泛化性能之间的平衡。

The conventional nonlinear system identification, referred to as the deterministic modeling method whose output is a single value(or a point output), and is incapable of dealing with the characteristics from a family of uncertain nonlinear functions or the systems with uncertain physical parameters. This paper proposed a novel method for identifying optimal interval regression model(OIRM) with sparsity to deal with the problem. The method combined sparsity stemming from the idea of structural risk minimization(SRM) principle, and used ?1-norm of approximation errors with some notions from linear programming(LP) problem. The optimization problems corresponding to URM and LRM with constraints in a form of convex inequality and linear equality were independently solved by LP. Finally, the sparsity and optimality of the proposed OIRM were demonstrated by the experimental cases using the two indices, the fractions of utilized support vectors(SVs) and root mean square error(RMSE). The proposed method not only could generate the optimal interval output, but also ensured the balance between identification accuracy and generalization performance of the OIRM.