In dynamic, complex and nonlinear systems, the analysis of transients, instabilities or unusual events is fundamental, as well as the knowledge of the system's behavior in the frequency space. What is usual in this type of study is to have discrete and digitally acquired data, due to a sampling process with a determined period or frequency. Extracting information from this data set is done by numerical methods, such as the Fourier Transform (FFT), the Hilbert‐Huang Transform (HHT) or techniques from chaos mathematics (Attractors). In this way we have scarce data, with some loss of information, analyzed with numerical techniques that introduce, also, some dilution of the information. In particular, the techniques of analysis in the frequency space, by their very nature, blur, frequencies and bandwidths. This leads in some cases to the identification of unsuitable or very wide frequencies or intervals, which make the extracted information unusable. To this effect, we have studied the VMD technique that provides more real and representative frequencies of the system as well as narrower bandwidths that make possible better identification of phenomena and influences. This technique has been applied to the analysis of thermohydraulic instabilities in nuclear boiling water reactors (BWR). The cases had already been analyzed with STFT and HHT techniques. The results of the application of the VMD shows that the mode mixing is solved, so modes obtained are monofrequency and these frequency bands are narrower than in previous methodologies. This improved performance allows using backbone plots for identifying which modes are excited in instabilities events.

中文翻译：

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使用变分模式分解的沸腾反应堆解析模式混合不稳定性分析

在动态，复杂和非线性系统中，对瞬态，不稳定性或异常事件的分析以及对系统在频率空间中的行为的了解是基础。由于具有确定周期或频率的采样过程，此类研究通常具有离散且以数字方式获取的数据。从此数据集中提取信息是通过数值方法完成的，例如傅立叶变换（FFT），希尔伯特-黄氏变换（HHT）或混沌数学中的技术（吸引子）。这样，我们就得到了数量有限的稀缺数据，并通过数值技术对其进行了分析，从而引入了一些信息稀释。特别是，频率空间中的分析技术本质上是模糊，频率和带宽。在某些情况下，这导致识别不合适或非常宽的频率或间隔，从而使提取的信息不可用。为此，我们研究了VMD技术，该技术可提供系统的更多实际频率和代表性频率以及更窄的带宽，从而可以更好地识别现象和影响。这项技术已应用于分析核沸水反应堆（BWR）中的热工水力不稳定性。病例已经通过STFT和HHT技术进行了分析。VMD的应用结果表明解决了模式混合，因此获得的模式是单频的，并且这些频带比以前的方法更窄。