基于超平面的T-S模糊模型辨识

针对多输入多输出(MIMO)的非线性热工动态对象,基于超平面的建模思想,提出了一种新的T-S模糊模型建模方法,既能够统一前、后件的参数辨识,又能防止过多增加计算量。介绍了通用的T-S模糊模型,详细推导出点到超平面的距离公式,据此,提出基于平均线性度的有效性能指标函数S(c),从而避免了规则数确定的盲目性。针对T-S模糊模型分段线性的特点,得出了输入、输出联合空间中的点到各后件子模型所对应的超平面距离,归纳出具体的建模步骤,同时给出了平均线性度D(c)的计算公式。新的建模算法可解释性好,不仅具有良好的精度,而且具有较好的泛化能力。最后,针对典型负荷被控对象的仿真结果证实了该方法的有效性。

T-S fuzzy model identification based on hyperplane

Aiming at the nonlinear thermal dynamic object with MIMO(Multi-Input Multi-Output),T-S fuzzy modeling method based on hyperplane is proposed,which unifies the antecedent and consequent parameters of T-S fuzzy model and prevents overabundance of calculation. The general T-S fuzzy model is introduced and the formula calculating the distance from a point to a hyperplane is deduced. The effectiveness index function S(c) based on the average linearity is proposed to determine the number of rules. The distances from an point to the hyperplanes corresponding to different consequent sub-models in the joint I/O space are obtained by the subsection-linearization of T-S fuzzy model and the modeling steps are concluded,as well as the formula of average linearity calculation. The new algorithm shows good interpretability,accuracy and generalization capability. The simulation of an object with typical load demonstrates its effectiveness.