Unsupervised health index estimation in rotating machinery via domain-constrained autoencoders with residual-based loss adaptation

Within Prognostics and Health Management (PHM), data-driven approaches are widely used to assess the condition of rotating machinery. However, constructing a reliable Health Index (HI) remains challenging particularly in unsupervised settings where explicit degradation labels are unavailable. Autoencoder-based methods can extract degradation-sensitive representations, but they often fail to produce HIs that are simultaneously monotonic, bounded, and physically consistent. Existing constrained approaches typically rely on manually tuned loss functions or optimizer-level modifications, which may lead to optimization conflicts and limited robustness. To address these limitations, this paper proposes a domain-constrained convolutional autoencoder for unsupervised HI estimation. The framework embeds trendability, monotonicity, and boundary constraints directly into the loss function and adaptively regulates their influence through a residual-based weighting mechanism. Unlike static penalty selection, the proposed strategy updates each constraint multiplier according to its observed violation during training, reducing the need for manual loss-weight calibration. A curriculum-guided initialization is further introduced to progressively enforce local constraints after the model has learned degradation-sensitive representations. The framework is validated on the PRONOSTIA and XJTU-SY datasets against a constrained autoencoder benchmark, demonstrating improved HI consistency and generalization. Although validated only on bearing datasets, the proposed weighting strategy is independent of the underlying architecture and may be extended to other PHM applications involving the joint optimization of multiple degradation-informed objectives.