  In both industrial and residential contexts, compressor-based machines, such
as refrigerators, HVAC systems, heat pumps and chillers, are essential to
fulfil production and consumers' needs. The diffusion of sensors and IoT
connectivity supports the development of monitoring systems that can detect and
predict faults, identify behavioural shifts and forecast the operational status
of machines and their components. The focus of this paper is to survey the
recent research on such tasks as FD, FP, Forecasting and CPD applied to
multivariate time series characterizing the operations of compressor-based
machines. These tasks play a critical role in improving the efficiency and
longevity of machines by minimizing downtime and maintenance costs and
improving the energy efficiency. Specifically, FD detects and diagnoses faults,
FP predicts such occurrences, forecasting anticipates the future value of
characteristic variables of machines and CPD identifies significant variations
in the behaviour of the appliances, such as a change in the working regime. We
identify and classify the approaches to the tasks mentioned above, compare the
algorithms employed, highlight the gaps in the current status of the art and
discuss the most promising future research directions in the field.
