This study proposes a novel integrated framework of physics-informed machine learning for virtual sensing in rotating machinery systems. The proposed framework aims to overcome the limitations of sparse physical measurements and enable comprehensive system monitoring. The proposed framework leverages a multi-fidelity data fusion strategy and physics-informed surrogate networks to achieve accurate and physically consistent predictions of dynamic responses across the entire domain under diverse operational conditions. The proposed framework comprises three key characteristics. First, a physics-constrained multi-agent diverse generative adversarial network (PC-MAD-GAN) is proposed to synthesize high-fidelity synthetic data. This architecture of a generative neural network effectively fuses extensive low-fidelity simulations datasets from finite element model (FEM), which provide full-field data across the system, with limited high-fidelity experimental measurements obtained from physically accessible regions. The multi-agent structure and physics constraints ensure that the generated synthetic data is both diverse and physically plausible, bridging the fidelity gap between simulation and reality. Second, a surrogate modeling scheme is introduced in the consideration of an adversarial domain adaptation architecture and a physics-informed domain-adversarial deep operator network (PI-DADON). This architecture is specifically designed for operator learning, enabling accurate interpolation and extrapolation of system dynamics, including responses under various rotating speeds, without requiring extensive retraining for unseen conditions. PI-DADON is trained on both the high-fidelity synthetic data and the limited real measurement data. Third, both the PC-MAD-GAN and PI-DADON architectures are rigorously supervised by the physics of rotating machinery. This strategy for physics-informed regularization is crucial to ensure that the model's predictions remain physically consistent and robust, even in unmeasured regions or under untrained operational conditions. The effectiveness of the proposed framework is comprehensively validated using dynamic response datasets obtained from an induction motor, including experiments under diverse operating conditions. Systematic analysis on experiments confirms that the proposed framework with physics-informed strategies significantly enhances accuracy, robustness, and generalization capability compared to purely data-driven approaches. The proposed framework facilitates the development of AI transformation for intelligent mechanical systems by enabling reliable virtual sensing in inaccessible areas, providing rich and full-field information critical for advanced condition monitoring and diagnosis.
Son et al. (Sun,) studied this question.