Condition monitoring is very important for critical assets such as gearboxes used in the power and mining industries. Fluctuating operating conditions are inevitable for wind turbines and mining machines such as bucket wheel excavators and draglines due to the continuous uctuating wind speeds and variations in ground properties, respectively. Many of the classical condition monitoring techniques have proven to be ine ective under uctuating operating conditions and therefore more sophisticated techniques have to be developed. However, many of the signal processing tools that are appropriate for uctuating operating conditions can be di cult to interpret, with the presence of incipient damage easily being overlooked. In this study, a cost-e ective diagnostic methodology is developed, using machine learning techniques, to diagnose the condition of the machine in the presence of uctuating operating conditions when only an acceleration signal, generated from a gearbox during normal operation, is available. The measured vibration signal is order tracked to preserve the angle-cyclostationary properties of the data. A robust tacholess order tracking methodology is proposed in this study using probabilistic approaches. The measured vibration signal is order tracked with the tacholess order tracking method (as opposed to computed order tracking), since this reduces the implementation and the running cost of the diagnostic methodology. Machine condition features, which are sensitive to changes in machine condition, are extracted from the order tracked vibration signal and processed. The machine condition features can be sensitive to operating condition changes as well. This makes it difficult to ascertain whether the changes in the machine condition features are due to changes in machine condition (i.e. a developing fault) or changes in operating conditions. This necessitates incorporating operating condition information into the diagnostic methodology to ensure that the inferred condition of the machine is not adversely a ected by the uctuating operating conditions. The operating conditions are not measured and therefore representative features are extracted and modelled with a hidden Markov model. The operating condition machine learning model aims to infer the operating condition state that was present during data acquisition from the operating condition features at each angle increment. The operating condition state information is used to optimise robust machine condition machine learning models, in the form of hidden Markov models. The information from the operating condition and machine condition models are combined using a probabilistic approach to generate a discrepancy signal. This discrepancy signal represents the deviation of the current features from the expected behaviour of the features of a gearbox in a healthy condition. A second synchronous averaging process, an automatic alarm threshold for fault detection, a gear-pinion discrepancy distribution and a healthy-damaged decomposition of the discrepancy signal are proposed to provide an intuitive and robust representation of the condition of the gearbox under uctuating operating conditions. This allows fault detection, localisation as well as trending to be performed on a gearbox during uctuating operation conditions. The proposed tacholess order tracking method is validated on seven datasets and the fault diagnostic methodology is validated on experimental as well as numerical data. Very promising results are obtained by the proposed tacholess order tracking method and by the diagnostic methodology. / Dissertation (MEng)--University of Pretoria, 2016. / Mechanical and Aeronautical Engineering / MEng / Unrestricted