CAJ | 학술논문

经验模式分解(EMD)及其改进算法作为实用的信号处理方法至今仍然缺少严格的数学理论。该文尝试从数学理论上分析集合经验模式分解和自适应噪声集合经验模式分解的重构误差，推导了总体残留噪声的计算公式。针对自适应噪声集合经验模式分解在每一层固有模态分量上仍然存在残留噪声的问题，在分解过程中添加成对的正负噪声分量，提出一种基于互补自适应噪声的集合经验模式分解算法。实验结果表明，相比于集合经验模式分解和自适应噪声集合经验模式分解，所提的方法能够明显地减少每一层固有模态分量中残留的噪声，拥有较好的信号重构精度和更快的分解速度。
경험모식분해(EMD)급기개진산법작위실용적신호처리방법지금잉연결소엄격적수학이론。해문상시종수학이론상분석집합경험모식분해화자괄응조성집합경험모식분해적중구오차，추도료총체잔류조성적계산공식。침대자괄응조성집합경험모식분해재매일층고유모태분량상잉연존재잔류조성적문제，재분해과정중첨가성대적정부조성분량，제출일충기우호보자괄응조성적집합경험모식분해산법。실험결과표명，상비우집합경험모식분해화자괄응조성집합경험모식분해，소제적방법능구명현지감소매일층고유모태분량중잔류적조성，옹유교호적신호중구정도화경쾌적분해속도。
Empirical Model Decomposition (EMD) and its improved algorithms are most useful signal processing methods. However, those methods still lack rigorous mathematical theory. This paper attempts to analyze mathematically the reconstruction errors for Ensemble EMD (EEMD) and EEMD with Adaptive Noises (EEMDAN). Moreover, the formulae of the residual noise are deduced step by step. There exists the residual noise in each intrinsic mode function during the EEMDAN. To suppress the residual noise, an improved ensemble empirical mode decomposition with complementary adaptive noises by adding pairs of positive and negative noises is proposed. The experimental results indicate that the proposed method can obviously reduce the residual noise in each intrinsic mode function compared with the EEMD and the EEMDAN, and it also has better signal reconstruction precision and faster signal decomposition.