带结构风险最小化的最优区间回归模型辨识

Identification of optimal interval regression model with structural risk minimization

中文关键词  结构风险最小化  逼近误差的$\ell_\infty$范数优化  最优区间回归模型  线性规划

英文关键词  structural risk minimization  $\ell_\infty$-norm optimization on approximation errors  optimal interval regression model  linear programming

中文摘要

      针对来自模型结构、参数以及测量数据的不确定性等因素, 传统的辨识方法获取的是确定性数学模型的点输出, 其鲁棒性差, 易受外界干扰. 因此, 采用区间输出比点输出更易于实际问题的研究. 基于复杂系统的不确定性测量数据以及系统参数的不确定性, 提出了最优区间回归模型辨识的一种新方法, 该方法将逼近误差的$\ell_\infty$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. 该方法在保证模型辨识精度的同时, 其泛化性能进一步得到提高. 实验分析表明, 提出的方法对来自噪声以及参数不确定性的数据, 可以从区间模型的辨识精度和泛化性能之间取其平衡.

英文摘要

      Aiming at the characteristics from a family of uncertain nonlinear functions or the systems with uncertain physical parameters, the problem of the conventional nonlinear system modeling , referred to as the deterministic modeling method whose output is a single value (or a point output), is prone to produce a poor robustness and is subject to external disturbance. This paper proposes a novel method for identifying optimal interval regression model (OIRM) with sparsity only based on the uncertain measurements of complex system. The OIRM, differently from standard deterministic models, is composed of upper regression model (URM) and lower regression model (LRM), and returns an interval output as opposed to a point output. The method combines sparsity stemming from the idea of structural risk minimization (SRM) principle, and optimality using $\ell_\infty$-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 are independently solved by LP. Finally, the equilibrium between modeling accuracy and generalization performance of the proposed OIRM are demonstrated by the experimental cases using the two indices, the fractions of utilised support vectors (SVs) and root mean square error (RMSE).