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回声状态网络(ESN)学习算法中可能存在解的奇异问题,在时间序列预测时易导致病态解问题,且伴随着具有较大幅值的输出权值,尤其是当训练样本个数小于输出权值维数时,ESN的解必为奇异的.鉴于此,考虑使用LM(Levenberg Marquardt)算法代替常用的线性回归方法,自适应选择LM参数,从而有效地控制输出权值的幅值,提高ESN的预测性能.通过Lorenz混沌时间序列进行预测研究,对大连月平均气温实际数据进行仿真研究,取得了较好的预测效果.
The singular problems that may exist in the ESN learning algorithm may lead to ill-posed problems in time series prediction, accompanied by output weights with larger amplitudes, especially when the number of training samples is less than the output weight The solution of ESN will be singular.In view of this, we consider the use of Levenberg-Marquardt (LM) algorithm instead of the commonly used linear regression method and choose the LM parameters adaptively, so as to effectively control the amplitude of output weights and improve the ESN Forecasting performance.The forecasting of Lorenz chaotic time series is carried out, and the actual data of monthly mean air temperature in Dalian are simulated and the good forecasting results are obtained.