LAUSR

In the field of signal processing, it is interesting to explore signal irregularities. Indeed, entropy approaches are efficient to quantify the complexity of a time series; their ability to analyze and provide information related to signal complexity justifies their growing interest. Unfortunately, many entropies exist, each requiring setting parameter values, such as the data length N, the embedding dimension m, the time lag τ, the tolerance r and the scale s for the entropy calculation. Our aim is to determine a methodology to choose the suitable entropy and the suitable parameter values. Therefore, this paper focuses on the effects of their variation. For illustration purposes, a brushless motor with a three-phase inverter is investigated to discover unique faults, and then multiple permanent open-circuit faults. Starting from the brushless inverter under healthy and faulty conditions, the various possible switching faults are discussed. The occurrence of faults in an inverter leads to atypical characteristics of phase currents, which can increase the complexity in the brushless response. Thus, the performance of many entropies and multiscale entropies is discussed to evaluate the complexity of the phase currents. Herein, we introduce a mathematical model to help select the appropriate entropy functions with proper parameter values, for detecting open-circuit faults. Moreover, this mathematical model enables to pick up many usual entropies and multiscale entropies (bubble, phase, slope and conditional entropy) that can best detect faults, for up to four switches. Simulations are then carried out to select the best entropy functions able to differentiate healthy from open-circuit faulty conditions of the inverter.