  With the current trend of increasing complexity of industrial systems, the
construction and monitoring of health indicators becomes even more challenging.
Given that health indicators are commonly employed to predict the end of life,
a crucial criterion for reliable health indicators is their capability to
discern a degradation trend. However, trending can pose challenges due to the
variability of operating conditions. An optimal transformation of health
indicators would therefore be one that converts degradation dynamics into a
coordinate system where degradation trends exhibit linearity. Koopman theory
framework is well-suited to address these challenges. In this work, we
demonstrate the successful extension of the previously proposed Deep Koopman
Operator approach to learn the dynamics of industrial systems by transforming
them into linearized coordinate systems, resulting in a latent representation
that provides sufficient information for estimating the system's remaining
useful life. Additionally, we propose a novel Koopman-Inspired Degradation
Model for degradation modelling of dynamical systems with control. The proposed
approach effectively disentangles the impact of degradation and imposed control
on the latent dynamics. The algorithm consistently outperforms in predicting
the remaining useful life of CNC milling machine cutters and Li-ion batteries,
whether operated under constant and varying current loads. Furthermore, we
highlight the utility of learned Koopman-inspired degradation operators
analyzing the influence of imposed control on the system's health state.
