Framework for stochastic modelling of long-term non-homogeneous data with non-Gaussian characteristics for machine condition prognosis

Abstract

To make prognosis one needs to build a model based on historical data. In the paper we propose a framework for modelling of long-term non-homogeneous data with non-Gaussian properties. These specific properties have been identified in real datasets describing the degradation process of the machine. The framework covers deterministic and random components separation, modelling of heavy-tailed, time-varying properties of random part as well as identification of possible autodependence hidden in the random sequence and identification of distribution for a random part. Due to non-linear trends, time-dependent scale (equivalent to the variance for Gaussian distributed data) and non-Gaussian characteristics present in the data, the final formula of the model is complex, its identification is challenging and requires specific, suitable to heavy-tailed processes, statistical methods. The paper provides two kind of novelties — first of all, it uses real data from condition monitoring systems and our findings may be novel and surprising to predictive maintenance community, secondly — processing such specific data opens new areas for general data modelling and highlight novel research directions.