Dependence structure analysis of the inverter operational data by means of copula theory

• We study inverter operational data which show unwanted resonance in speed signal.
• Copula theory is applied to model dependence between signals.
• Correlation between the resonance and system signals is found through copulas.
• Graphical and numerical methods are used to verify goodness of the fit.

The dependence structure between various signals produced by a mechanical system can have in principle a very complex form. In order to reveal statistical information hidden in data, we apply the copula theory, which is a general way of representing dependence structure for multivariate distributions. The proposed framework is demonstrated through a case study of the inverter operational data. Particularly, for the initial analysis of dependencies we use graphical and numerical rank-based methods. Moreover, for the selected pair of signals we estimate parameters of three copula models, and validate the results against the goodness-of-fit test procedure. It is concluded that only one model reflects the dependence structure accordingly and the obtained estimates show correlation with faulty behavior of the system.