Correlation analysis for impedance-based health monitoring of electromagnetic coils

Electromagnetic coils are widely used components in a variety of industries and systems, including electric motors and solenoids. The failure of electromagnetic coil insulation can lead to catastrophic failure of the coil and subsequently, the component and system in which the coil is used. In this paper, a method of locating frequencies in the impedance spectrum that are not only useful for health monitoring, but reveal the changing electrical behavior of coil due to degraded wire insulation is demonstrated. The Spearman rank correlation coefficient can be used to measure linear or non-linear monotonic relationships between two variables. Hence, the measure is more general than the Pearson correlation coefficient, which measures only the linear correlation between two variables. First, experiments were performed where electromagnetic coils were subjected to degrading environments while measuring the impedance spectra of the coils. These complex impedance spectrum measurements are split into real and imaginary parts, resistance and reactance, respectively. The values of resistance and reactance at each frequency constitute a set of features, each of which is a potential health indicator. Second, the impedance time series at each frequency is correlated with degradation time using Spearman correlation. Next, the Spearman correlation coefficient is plotted against frequency to construct an impedance frequency-correlation diagram, providing an understanding of the extent to which each frequency can be used to monitor the health of the coil, and whether the impedance at each frequency increases or decreases over the aging period. The results indicate that the Spearman correlation coefficient is a tool that can be utilized to identify the frequencies at which to monitor the coil for health monitoring purposes. Furthermore, comparisons between environmental aging tests show the impedance frequency-correlation diagrams can be applied in understanding the mechanisms of degradation.