Invertible transfer function informed neural ODE to learn stable latent dynamics for degradation process modeling and remaining useful life prediction

Abstract

Modeling degradation processes is essential for estimating industrial system performance and guiding maintenance decisions. Machine learning methods, due to the adaptability for diverse data types, show promise to model temporal evolution of degradation in an embedding space known as latent dynamics, especially for neural ordinary differential equations (NODE) with continuous-time property. However, inferring system states from observation data is an inverse problem, and NODEs often inherit ill-posedness further from their complex optimization landscape. We propose an invertible transfer function informed NODE to ensure stable latent dynamics, making the model robust to perturbations in observation data. First, a NODE describes the hidden degradation process, while an invertible Fourier neural operator maps between latent dynamics and observations. Error analysis reveals that stability is governed by data fidelity and the Lipschitz constant of the inverse mapping, forming the basis for our regularization technique. Additionally, we demonstrate that without ground truth degradation data, latent dynamics lack uniqueness, leading to infinite equivalent solutions. Tests on turbofan engine and battery datasets confirm improved robustness and performance in fault diagnosis and prognosis.