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自然界中观测到的混沌现象一般都混有噪声,存在的噪声会使得对混沌时间序列的预测产生较大的误差。小波阈值去噪具有多分辨率分析的特点,计算量较小,同时去噪效果较好,但传统的消噪方法存在重信号而轻噪声特征的情况,噪声水平的估计也常常以第1层小波系数的中值变差为依据,同时阈值的选取又与噪声水平和信号长度相关。如果能准确估算混沌信号的水平,并确定各层小波分解系数上的噪声方差,便可提高去噪效果。因此,构建了近似仿真Lorenz混沌含噪信号,并通过极大重叠离散小波对信号进行了分解,分析噪声方差在各层小波系数上的分布规律,并由此确定小波系数各层不同的阈值系数。通过该方法可以得到相对较优的结果。算例结果表明,采用所提方法可以减少预测产生的误差,验证了该方法的有效性。
The observed chaos in nature is generally mixed with noise, the existence of noise will make the prediction of chaotic time series have a greater error. Wavelet threshold denoising has the characteristics of multi-resolution analysis, the calculation is small, and the de-noising effect is better, but the traditional de-noising method has the characteristics of heavy signal and light noise. The estimation of noise level is often based on the first layer The median variation of wavelet coefficients is the basis, meanwhile, the selection of threshold is related to noise level and signal length. If we can accurately estimate the level of chaotic signal, and determine the noise variance of wavelet decomposition coefficient of each layer, we can improve the denoising effect. Therefore, an approximate simulation Lorenz chaotic and noisy signal is constructed, and the signal is decomposed by highly overlapping discrete wavelet to analyze the distribution rule of noise variance on each layer of wavelet coefficients, and then the different threshold coefficients of each layer of wavelet coefficients . This method can be relatively good results. The results show that the proposed method can reduce the error caused by the prediction and verify the effectiveness of the method.