A root location-based framework for degradation modeling of dynamic systems with predictive maintenance perspective

Abstract

This paper considers dynamic systems widely used in industry for which the behavior can be approximated to a second order differential equation. The components of such a system suffer from random faults and failures due to wear, age or usage. These events impact the dynamic behavior which is interpreted as a modification of the initial differential equation with random coefficients. At given times, the system is solicited and its output – the only source of information – is measured to infer the position of equation roots in the complex plane. The Euclidian distance between the current and initial positions of a root is proposed as a new indicator reflecting the gradual deterioration of system performance. Such an indicator presents stochastic trajectories in time according to the random evolution of the root location in complex plane. More especially, these trajectories can be modeled by an univariate non-linear diffusion process if underlying degradation sources are assumed to be homogeneous Gamma processes. Based on this model, the system remaining useful lifetime is assessed. Two predictive maintenance policies are also designed showing the feasibility to easily maintain dynamic systems solely on the system output.