Abstract In this paper, a novel Multivariate Nonlinear Chirp Mode Decomposition (MNCMD) is proposed. In contrast to most existing multivariate time-frequency decomposition approaches, the proposed MNCMD is capable of handling time-varying signal efficiently in an elegant variational optimization framework. The multivariate nonlinear chirp mode is defined based on the presence of a joint or common instantaneous frequency component among all channels of input signal. Then the objective function of MNCMD is defined as the sum of mode bandwidths across all signal channels. The alternate direction method of multipliers (ADMM) algorithm is employed to optimize the MNCMD problem. MNCMD can extract an optimal set of multivariate modes and their corresponding instantaneous frequencies without requiring more user-defined parameters than the original NCMD. The effectiveness and advantages of the proposed MNCMD are demonstrated by studying its mode-alignment, filter bank structure, quasi-orthogonality, the influence of channel number, noise robustness, and convergence. Specifically, we highlight the utility and superiority of the proposed method in three real-world applications, including the analysis of an oceanographic float position record (two-channel), the separation of α-rhythms in electroencephalogram (EEG) data (four-channel), and the detection of plant-wide oscillations in industrial control systems (nine-channel).

中文翻译：

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多元非线性啁啾模式分解

摘要 本文提出了一种新的多元非线性啁啾模式分解(MNCMD)。与大多数现有的多元时频分解方法相比，所提出的 MNCMD 能够在优雅的变分优化框架中有效地处理时变信号。多元非线性啁啾模式是根据输入信号的所有通道之间是否存在联合或公共瞬时频率分量来定义的。然后将 MNCMD 的目标函数定义为所有信号通道上模式带宽的总和。乘法器交替方向法（ADMM）算法被用来优化MNCMD问题。MNCMD 可以提取一组最优的多元模式及其相应的瞬时频率，而不需要比原始 NCMD 更多的用户定义参数。通过研究其模式对齐、滤波器组结构、准正交性、信道数的影响、噪声鲁棒性和收敛性，证明了所提出的 MNCMD 的有效性和优势。具体来说，我们强调了所提出的方法在三个实际应用中的实用性和优越性，包括海洋浮标位置记录的分析（双通道）、脑电图（EEG）数据中 α 节律的分离（四通道） )，以及工业控制系统中全厂振荡的检测（九通道）。