DiFG-Net++: Physics-Informed Functional Learning for Self-Supervised and Domain-Adaptive Fault Diagnosis

Abstract

Cross-speed fault diagnosis remains a significant challenge in data-driven prognostics and health management (PHM) because vibration signatures and fault characteristic frequencies vary systematically with rotational speed. The problem becomes particularly difficult in open-set scenarios where the target operating speed lies outside the range observed during training and fault data at the target speed are unavailable. Although recent advances in self-supervised learning (SSL), particularly Prediction of Functionals from Masked Latents (PFML), have demonstrated promising capabilities for learning fault-sensitive representations from unlabeled data, existing PFML-based frameworks do not explicitly address speed-induced distribution shifts. In particular, the recently developed Domain-Informed Functional Guidance Network (DiFG-Net) relies primarily on handcrafted functionals and lacks mechanisms for enforcing speed-invariant representation learning.

To address these limitations, this paper proposes DiFG Net++, a physics-informed functional learning framework specifically designed for open-set cross-speed fault diagnosis. Building upon the DiFG-Net architecture, DiFG Net++ integrates three complementary speed-adaptation strategies: (1) speed-extrapolative augmentation, which generates
physically meaningful intermediate and extrapolated speed conditions through speed-guided time scale transformations; (2) speed-invariant latent regularization, which encourages latent representations associated with the same machine health condition to remain consistent across operating speeds; and (3) healthy-state target-speed anchoring, which leverages readily available healthy vibration data at the target operating speed to facilitate adaptation without requiring target-speed fault samples. In addition, order-domain functionals are incorporated as physics-informed self-supervised targets to promote learning of speed-robust fault characteristics. 

The effectiveness of the proposed framework is evaluated on a plastic-bearing fault dataset collected at four rotational speeds and across multiple bearing health conditions.  Experimental results demonstrate that the proposed speed adaptation mechanisms substantially improve open-set cross-speed fault diagnosis performance. Compared with the baseline DiFG-Net, which achieved an overall validation accuracy of 46.68%, the proposed DiFG-Net++ achieved an overall accuracy of 95.85%, representing a relative improvement of more than 105%. These results demonstrate that integrating physics-informed functional learning with speed-aware representation learning provides an effective and practical solution for robust cross-speed fault diagnosis under previously unseen operating conditions.