Deep Koopman Operator-based degradation modelling

TL;DR

This paper extends Deep Koopman Operator theory to model industrial system degradation, transforming complex dynamics into linear forms for better health monitoring and RUL prediction, even under varying control conditions.

Contribution

It introduces a novel Koopman-Inspired Degradation Model that disentangles degradation effects from control influences, improving RUL prediction accuracy in industrial systems.

Findings

Outperforms existing methods in predicting RUL of CNC milling cutters and Li-ion batteries.

Effectively disentangles degradation from control effects in latent space.

Demonstrates utility of Koopman operators in health state analysis.

Abstract

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.