Degradation Assessment of Drilling Head based on Stochastic Growth Models and Continuous Time Diffusion Processes

Degradation is a phenomenon which necessarily accompanies the operation of every mechanical system. The monitoring of the degradation level is not simple, since it is not always possible to track the wear directly. Therefore the degradation is sometimes examined by applying indirect measures. In our article we study the degradation of a mining drilling machine. We focus on the wear level of cutting tools. We have the data records about the operation of this machine. Using selected stochastic growth models, we study the trend in the development of cutting tools wear. These models provide us with the key parameters of the trend – a mean value, a variance, and standard deviation, which we later use in specific diffusion models. Applying these diffusion models, we examine the trajectories of the degradation wear, up to the possible moment of the first hitting time (FHT). This moment is the point when a cutting tool reaches its critical level. Although this does not necessarily lead to the occurrence of a hard failure but a soft failure, it significantly aggravates the operation properties of a system.