基于结构风险最小化的TS模糊模型辨识研究

Research on Identifying TS Fuzzy Model Based on Structural Risk Minimization

针对TS模糊模型的后件参数辨识,为了避免传统意义上以经验风险最小化来求解参数,同时考虑到如何控制模型结构复杂性以及经验风险又要最小,提出了一种基于最小二乘支持向量回归(LSSVR)结构风险分解建立新的代价函数来辨识TS模糊模型。紧接着,以该代价函数作为优化目标,TS模糊模型为约束条件,通过引入拉格朗日方法对其求解,最终得到模型的后件参数。该方法有如下显著特征:1)引出的代价函数是基于结构风险而非经验风险;2)计算过程不仅避免了核函数的选择,而且仅对原输入数据空间做内积;3)全局与局部性能得到保证。最后,论证了该方法的有效性和优越性。

Aiming at the consequent parameters of the TS fuzzy model,a novel cost function based on decomposing LSSVR was proposed to identify consequent parameters,which makes use of the structural risk considering how to control the trade-off between empirical risk and model complexity instead of the conventional empirical risk. And then,a new optimization problem was formulated by treating the obtained cost function as the objective function,TS fuzzy model as constraint condition,and the consequent parameters of TS fuzzy model were derived by applying Lagrange method. The resulting method has the following distinct features：（ 1） the obtained new cost function can be regarded as a structural risk instead of empirical risk;（ 2） the computation process cannot only avoid the selection of kernel function,but also merely use the scalar product for original input space; and（ 3）the approach can well guarantee the performance of both local-regression models and global model. Finally,the viability and superiority of the method were verified by simulation.