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.