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对于含噪混沌时间序列预测问题,传统方法存在较大的经验性,对预测误差的构成分析不足,因而忽略了混沌动态重建与预测模型建立之间的差异性.本文将实际预测误差分解为预测器偏差和输入扰动误差,并对整体最小二乘和正则化两种全局预测方法进行分析比较,进而说明整体最小二乘适用于混沌动态的重建,对预测器偏差影响较大,而正则化方法能够改善预测器敏感性,对输入扰动误差影响较大.通过两个仿真实例,展示了混沌动态重建与预测模型建立之间的差异,在对比最小二乘和正则化方法的同时验证了实际预测误差受预测器偏差和输入扰动误差共同作用.并指出,在实际操作时应在二者间寻求平衡,以便使模型预测精度达到最优.
For the prediction of time series with noisy chaos, the traditional method has a large empirical and the analysis of the composition of the prediction error is not enough, thus ignoring the difference between the chaotic dynamic reconstruction and the establishment of the prediction model.In this paper, the actual prediction error is decomposed into the prediction The results show that the global least squares method is suitable for the reconstruction of chaotic dynamics and has a great influence on the predictor bias. However, the regularization method Which can improve the sensitivity of the predictor and greatly affect the input disturbance error.Through two simulation examples, the difference between the establishment of the chaotic dynamic reconstruction and the prediction model is demonstrated, and the actual prediction is validated by comparing with the least-squares and regularization methods The error is affected by the predictor deviation and the input disturbance error, and points out that in actual operation, the balance should be found between the two in order to optimize the model prediction accuracy.