This report presents a novel framework for anomaly detection in mechanical systems under time-varying operating conditions, addressing the challenge of operating condition-health information entanglement that often leads to false alarms or missed detections. Motivated by the need for reliable health monitoring across dynamic operational scenarios, two unsupervised disentanglement-based approaches are proposed.

First, a Conditional Feature Disentanglement Variational Autoencoder (FDCVAE) is developed to utilize available operating condition information as an inductive bias, enabling the separation of condition-related and health-related latent features. Experimental results from time-varying speed bearing fatigue tests demonstrate the model's ability to suppress operating condition interference and accurately detect incipient anomalies, as validated through spectral kurtosis analysis and health indicator comparisons.

Second, for scenarios where operating condition information is missing, a Dispersed Regularization VAE (DR-VAE) is introduced, leveraging prior-driven disentanglement by enforcing heterogeneous constraints on latent variables. This method achieves robust feature separation without external operating condition inputs, validated through multi-sensor simulations and real-world gantry crane fault detection.

Comparative experiments show that the proposed methods significantly outperform traditional models in both early fault detection and generalization across variable conditions. However, limitations remain in the disentanglement of degradation information during long-term evolution, pointing to future research directions for modeling dynamic entanglement between health progression and operating conditions.