A time–frequency Koopman-constrained variational encoder for interpretable remaining useful life prediction

Abstract

Remaining useful life (RUL) prediction supports failure prevention and maintenance planning for industrial equipment. Although variational autoencoder-based methods provide a latent-space pathway for interpretable RUL prediction, their encoders still mainly rely on time-domain information, which makes it difficult to capture frequency-domain features associated with global degradation trends. In addition, latent degradation trajectories often lack explicit dynamic constraints, weakening the trend consistency and interpretability of the learned representations. To address these issues, this paper proposes a time–frequency Koopman-constrained variational encoding model, termed TFK-VAE, for interpretable RUL prediction. TFK-VAE first constructs a time–frequency embedding module, which extracts sparse frequency-domain components related to degradation through an adaptive discrete cosine transform and fuses them with time-domain information to represent nonstationary signals. Then, a Transformer-based variational encoding network learns compact latent degradation representations from the fused features. The model introduces a Koopman-constrained hierarchical latent space, which regularizes latent trajectories through linearized degradation dynamics in a low-dimensional space. Experiments on turbofan engine and bearing degradation datasets show that TFK-VAE achieves superior or competitive performance in terms of root mean square error and score function. Latent-space visualization indicates that the proposed model forms interpretable degradation trajectories, thereby supporting accurate life prediction and transparent health state assessment.