Classical Empirical Mode Decomposition (EMD) is a data-driven method used to analyze non-linear and non-stationary time series data. Besides being an adaptable method by its nature, EMD assumes that every data consists of oscillations of the intrinsic mode functions (IMF). EMD also requires the condition that IMFs which represent the characteristic structures in the data should show only a unique sub-characteristic of the data. However, in some cases, depending on the way the sub-characteristics which make up a sophisticated data coexist, the IMFs are able to be not unique. This is called the mode-mixing problem. Although there are many studies and successful methods (such as EEMD, CEEMDAN) for eliminating the mode-mixing problem, a limited number of studies exist on determining the presence of the aforementioned problem. In this study, a method for the determination of the mode-mixing problem is proposed. In the suggested method, the Itakura–Saito distance, which is a measurement of the similarity of stationary signals and based on Fourier spectrums, is modified by applying Kaiser filter onto short-time signals. The performance of the method is tested via various applications with simulated and real data, and the results show successful detection of the mode-mixing if it exists in time series.

经典经验模态分解 (EMD) 是一种数据驱动的方法，用于分析非线性和非平稳时间序列数据。除了本质上是一种适应性强的方法外，EMD 还假设每个数据都包含固有模式函数 (IMF) 的振荡。EMD 还要求表示数据中特征结构的 IMF 应仅显示数据的唯一子特征。然而，在某些情况下，根据构成复杂数据的子特征的共存方式，IMF 可能不是唯一的。这称为模式混合问题。尽管有许多研究和成功的方法（如 EEMD、CEEMDAN）来消除模式混合问题，但关于确定上述问题的存在的研究数量有限。在这项研究中，提出了一种确定模式混合问题的方法。在建议的方法中，通过对短时信号应用 Kaiser 滤波器来修改 Itakura-Saito 距离，它是对静止信号相似性的测量并基于傅里叶谱。该方法的性能通过模拟和真实数据的各种应用程序进行测试，结果表明如果模式混合存在于时间序列中，则成功检测到模式混合。