基于分数阶滤波器的高泛化性神经网络建模

High Generalization Neural Network Modeling Based on Fractional Order Filter

为了显著提高神经网络建模的泛化性,提出了激活函数是分数阶滤波器的神经网络。分数阶滤波器涵盖了Butterworth和Chebyshev滤波器的性能。滤波器集对样本信号进行频率分解,既提升了信息的致密性,也保证了遍历性,更有助于提高神经网络的泛化性。各滤波器参数由盲动粒子群优化算法寻优。神经网络解算时,既采用了线性回归求解神经网络输出层权重,又在有限频段上用线性传递函数模拟替代分数阶传递函数,这两种措施缩短了解算时间。仿真结果表明,线性系统的泛化性精度可达亿分之几,非线性系统可达万分之几,可以离线应用。

In order to improve the generalization of neural network modeling significantly, a neural network that activation function is fractional order filter is proposed. The fractional order filter coveres the properties of Butterworth and Chebyshev filters. Because the signal frequency of the sample is decomposed by the filter set, the information compactness is enhanced and the ergodicity is ensured, which helps to improve the generalization of neural network. The parameters of each filter are optimized by particle swarm optimization with blindfold feature. In order to save the computation time of the network, the linear regression algorithm is used to solve the output layer weight of the neural network, and the linear transfer function is used to replace the fractional order transfer function in the finite frequency band. The simulation results show that the generalization accuracy of the linear system is up to parts per hundred million, and the nonlinear system can be up to parts per ten thousands, so it can be used offline