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Hilbert versus Concordia transform for three-phase machine stator current time-frequency monitoring

机译：Hilbert vs Concordia变换用于三相电机定子电流时频监测

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This paper deals with mechanical fault diagnosis in three-phase induction machines from stator current measurements. According to machine models, mechanical faults lead to amplitude and/or phase modulations of the measured stator current with possibly time varying carrier frequency. The modulation diagnosis requires a univocal definition of the instantaneous phase and amplitude. This is performed by associating a complex signal to the real measured one. For a convenient separate modulation diagnosis, the complex signal instantaneous phase and amplitude are expected to carry, respectively, information about the phase and amplitude modulations. The complex signal is classically obtained through the Hilbert transform. Under Bedrosian conditions, the so-called analytic signal allows a separate modulation diagnosis. However, mechanical faults may also produce fast modulations violating the Bedrosian conditions. This study proposes an alternative complex signal representation which takes advantage of the three stator current measurements available in a three-phase machine. From two stator current measurements, the Concordia transform builds a complex vector, the so-called space vector, which unconditionally allows separate modulation diagnosis. This paper applies and compares the Hilbert and Concordia transforms, theoretically and in case of simulated and experimental signals with various modulation frequency ranges.
机译：本文根据定子电流测量结果对三相感应电机的机械故障进行诊断。根据机器模型，机械故障会导致所测量的定子电流在可能随时间变化的载波频率下发生幅度和/或相位调制。调制诊断需要明确定义瞬时相位和幅度。这是通过将复杂信号与实际测量信号相关联来执行的。为了方便进行单独的调制诊断，复合信号的瞬时相位和幅度应分别携带有关相位和幅度调制的信息。复数信号通常通过希尔伯特变换获得。在贝德罗斯条件下，所谓的分析信号允许进行单独的调制诊断。但是，机械故障也可能会产生违反贝德罗斯条件的快速调制。这项研究提出了一种替代的复杂信号表示形式，它利用了三相电机中的三个定子电流测量值。通过两次定子电流测量，Concordia变换可建立一个复数向量，即所谓的空间向量，该向量无条件地允许进行单独的调制诊断。本文在理论上以及在具有各种调制频率范围的模拟和实验信号的情况下，应用并比较了希尔伯特和康科迪亚变换。

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