保泛化性能的最优上边界回归模型辨识

Optimal Upper Boundary Regression Model Identification with Generalization Performance-Guaranteed

从控制模型结构复杂性及提高模型辨识精度出发,提出了建模由参数或测量不确定性引起的最优上边界回归模型的一种新方法.首先,将二次规划的支持向量回归(SVR,support vector regression)转化为l1范数的优化问题,用于获取模型结构的稀疏解;其次,建立上边界回归模型的约束条件,并将模型的被估输出与实际输出之间的所有逼近误差最小化,即逼近误差的l1范数最小化问题,来提高模型辨识精度;最后,将l1范数的结构风险与逼近误差的l1范数以及上边界回归模型约束条件相结合构成新的优化问题,应用较简单的线性规划对其求解,得到最优上边界回归模型.提出的方法具有如下三个显著特性:1)应用逼近误差的l1范数最小化,可保证模型的建模精度;2)引入SVR架构下的结构风险l1范数,可保证模型的稀疏特性;3)通过提出的方法从建模精度与模型稀疏特性之间取其平衡,可提高模型泛化性能.通过来自测量数据以及模型参数不确定性的实验分析,论证了提出方法的合理性与优越性.

From the point of view of dominating the model structure and improving the identification accuracy,a new modelling method to construct optimal upper boundary regression model(UBRM)is proposed.Firstly,quadratic programming-support vector regression(QP-SVR)is converted to the optimization of l1-norm to obtain the sparsity of the UBRM.Secondly,constraints corresponding to the UBRM and l1-norm on approximation errors are constructed to improve the identification accuracy.Finally,a new optimization problem combined the structural risk of l1-norm with l1-norm on approximation errors is thus formulated and it is solved by linear programming to derive an optimal UBRM.The optimal UBM has the following remarkable features:1)modelling accuracy of UBRM can be guaranteed by the l1-norm minimization on approximation error;2)model structural complexity is under control by introducing l1-norm on structural risk within the framework of support vector regression(SVR)to guarantee the model sparsity;3)the generalization performance of the proposed method adopts the equilibrium between the modelling accuracy and sparseness.The rationalities and superiorities of the proposed optimal UBRM is demonstrated by experiments derived from uncertain measurements and uncertain parameters of nonlinear system.