基于鲁棒回声状态网络的混沌时间序列预测研究

摘要

Focusing on the problem that the echo state network is easily influenced by outliers,in this paper we propose a robust model based on the Laplace prior distribution.This is achieved by replacing the Gaussian distribution with the Laplace distribution as the prior of the model output,the Laplace prior is less sensitive to the outliers and can enhance the capbility of the model to restrict outliers.Furthermoer,to solve the problem arising from the introduction of the Laplace distribution,which makes the solving process of the method difficlut,the bound optimization algorithm is employed and a suitable surrogate function is established.Based on the bound optimization algorithm,the Laplace prior can be equivalently transformed into the form of Gaussian prior,which is easily computed,and it can also be use to estimate the model parameters adaptively.Simulation results illustrate that the proposed method can be robust when outliers exist,while remaining acceptable prediction accuracy.%针对回声状态网络模型易受异常点影响的问题,提出一种基于拉普拉斯先验分布的鲁棒回声状态网络模型.通过采用对异常点不敏感的拉普拉斯分布代替高斯分布作为模型输出的先验,以增强网络对于异常点的抑制能力.此外,为解决由引入拉普拉斯分布所造成的求解困难的问题,根据边际优化方法,构建适当的替代函数,使拉普拉斯先验等价转化为易于计算的高斯形式,并通过贝叶斯方法实现模型参数的自适应估计.仿真结果表明,在异常点存在的情况下,本文所提出的模型具有较好的鲁棒性,并仍能保持较高的预测精度.