基于概率信息与协作学习的鲁棒T-S模糊建模方法

Robust T-S Fuzzy Modeling Method Based on Probability Information and Collaborative Learning

T-S模糊建模方法在非线性系统建模中取得了大量的应用.然而,T-S模型在参数辨识过程中忽略了结构风险项,同时没有考虑各个规则之间的联系,因此在数据受到非高斯噪声和异常点的影响时,模型容易失效.针对以上不足,提出了基于概率信息与协作学习的模糊建模方法.该方法建立了规则之间协作学习机制以保证模型的连续性、平滑性与鲁棒性,并进一步构建了包含正则化项、误差项、规则概率信息及规则之间协作关系项的目标函数,用于提高模型的泛化能力和建模性能.除此之外,建立了空间投影机制,将数据低维特征空间的非线性关系转换为高维投影空间的线性关系,以增强规则之间的协作性.针对该模型,建立了基于最小二乘的求解方法,获得了可靠的模型参数.数学算例仿真和实际锻压实验表明:所提出的方法在面对噪声以及强非线性影响时,依然能在规则数较低的情况下保持优秀的建模性能.对比其他优秀的模糊建模方法,该模型有着更强的抗干扰能力,且建模均方根误差(RMSE)远低于其他建模方法.综上所述,所提出的方法对传统方法和建模理论进行了改进,即使面对强非线性系统拥有较强的泛化能力、鲁棒性以及优秀的建模能力,并且能够以较少的模糊规则对工程当中非线性、不确定性系统建模.

The T-S fuzzy modeling method has been widely implemented in nonlinear system modeling.However,in the process of parameter identification,the T-S model ignores structural risk items and does not consider the relationship between the fuzzy rules,making the model prone to failure when the data is affected by non-Gaussian noise and outliers.A fuzzy modeling method based on probability information and collaborative learning is proposed to address the above mentioned shortcomings.Specifically,a collaborative learning mechanism between rules is established to ensure the continuity,smoothness,and robustness of the model,and an objective function including regularization term,error term,rule probability information,and collaborative relationship term is further constructed to improve the model’s generalization capability and modeling performance.Moreover,a space projection mechanism is established to transform nonlinear relationships in the low-dimensional space into linear relationships in the highdimensional projection space to improve rule collaboration.A solution method based on least squares is established to solve this model and obtain reliable model parameters.The proposed method exhibits excellent modeling performance with low rule numbers under noise and a strong nonlinearity environment,as shown by mathematical example simulation and practical forging experiments.Compared to other excellent fuzzy modeling methods,the model has stronger anti-interference capability and the modeling root mean square error(RMSE)is much lower.In summary,the proposed method enhances traditional methods and modeling theory,and it possesses strong generalization,robustness,and excellent modeling capability for strongly nonlinear systems,which can effectively model nonlinear and uncertain systems in engineering with fewer fuzzy rules.