基于噪声辅助非均匀采样复数据经验模态分解的混沌信号降噪

摘要

鉴于非均匀采样复数据经验模态分解(NSBEMD)相对传统分解方法的优势和噪声的NSBEMD特性,提出了一种基于噪声辅助NSBEMD的混沌信号自适应降噪方法。该方法首先以含噪混沌信号和高斯白噪声分别为实、虚部来构造复数据并进行NSBEMD,然后根据虚部各IMF的能量来估算实部各IMF中包含的噪声能量,最后根据噪声能量的估计值对实部IMF进行奇异值分解(SVD)降噪。噪声估计实验验证了噪声能量估计方法的可行性,而Lorenz信号和太阳黑子月平均数的降噪实验则表明,相对于现有EMD降噪方法,本文方法能够进一步消除噪声,更清晰地恢复出混沌吸引子的拓扑结构。%According to the advantages of nonuniformly sampled bivariate empirical mode decomposition and the characteris-tics of noise after it, an adaptive chaotic signal denoising method is proposed based on the noise-assisted nonuniformly sampled bivariate empirical mode decomposition. Firstly, a complex signal is constructed for the noise-assisted nonuni-formly sampled bivariate empirical mode decomposition, by using noisy chaotic signal and gaussian white noise as the real part and imaginary part respectively; secondly, the noise energy of each intrinsic mode function in the real part is estimated according to the energy of each intrinsic mode function in the imaginary part; and finally, from the above results, each intrinsic mode function in the real part is denoised by using the singular value decomposition. Noise en-ergy estimate numerical experiment validates the feasibility of this method, and the denoising tests for Lorenz signal and monthly sunspot data indicate that our method shows advantages in both noise reduction and chaotic attractor topological configuration reversion.