Selection of the level of vibration signal decomposition and mother wavelets to determine the level of failure severity in spur gearboxes

Spur gearboxes are an integral component in the operation of rotary machines. Hence, the early determination of the severity level of a failure is crucial. This manuscript delineates a methodology for selecting essential mother wavelets and filters from the wavelet transform (WT) to process the vibration signal within the time-frequency domain, aiming to ascertain the severity level of failures in spur gearboxes. Initially, information is garnered from the gearbox through vibration signals in the time domain, utilising six accelerometers. Subsequently, the signal is partitioned into various levels, and information from each level is extracted using diverse mother wavelets and their respective filters. The signal is segmented into sub-bands, from which the condition state is ascertained using an energy operator. After that, the appropriate level of wave decomposition is determined through ANOVA tests and post-hoc Tukey analyses, evaluating performance in failure classification via the Random Forest (RF) model. Upon establishing the decomposition level, the analysis proceeds to identify which mother wavelets and filters are most suitable for determining the severity level of different types of failure in spur gearboxes. Moreover, this study investigates the impact of sensor positioning and inclination on acquiring the vibration signal. This aspect is explored through factorial ANOVA tests and multiple comparisons of the data derived from the sensors. The RF classification model achieved exceedingly favourable results (accuracy (Formula presented.) 96% and AUC (Formula presented.) 98%), with minimal practical influence from the positioning and inclination of a sensor, thereby affirming the proposed methodology's suitability for this type of analysis.