基于稀疏化核方法的非线性动态系统在线辨识

为了抑制辨识模型阶数的不断增长,适应系统的时变动态特征,以滑动时间窗为基本建模策略,提出了一种具有自适应正则化因子的核超限学习机(kernel extreme learning machine, KELM)在线辨识方法。通过构建新的目标函数,使得正则化因子可以随着系统动态而改变,保证了模型在不同的非线性区域拥有不同的结构风险;通过构建统一的学习框架,在保证每一次训练迭代中学习过程稀疏化的同时,实现了核权重系数与正则化因子的同步更新。实验结果表明，提出的方法相比与其他基于KELM的在线序贯学习方法,在有无噪声的情况下,均可以有效提升辨识精度,并且具有更好的稳定性。

Nonlinear system online identification based on kernel sparse learning#br# algorithm with adaptive regulation factor

In order to curb the continuous growing of model network size and effectively adapt to real-time system variation, an online sparse kernel extreme learning machine (KELM) with adaptive regulation factor is proposed to model time-varying nonlinear systems. Construction of a new objective function makes the model have different structural risks in different nonlinear regions and ensures the regulation factor vary over time with the time-varying nonlinear dynamics. A three-step solving method is used to determine the sparse dictionary and current optimal regulation factor. The proposed method has the capability of online updating both the kernel weight coefficient and the regulation factor vector. The effectiveness of the proposed method is demonstrated through applying it to the modeling of a practical case. Comparisons between the proposed method and existing KELM-based modeling methods indicate that the proposed method can effectively improve modeling accuracy and has better stability.