Condition monitoring of rotating shafts is essential for ensuring the reliability and optimal performance of machinery in diverse industries. In this context, as industrial systems become increasingly complex, the need for efficient data processing techniques is paramount. Deep learning has emerged as a dominant approach due to its capacity to capture intricate data patterns and relationships. However, a prevalent challenge lies in the black-box nature of many deep learning algorithms, which often operate without adhering to the underlying physical characteristics intrinsic to the studied phenomena. To address this limitation and enhance the fusion of data-driven methodologies with the fundamental physics of the system under study, this paper leverages physics-informed neural networks (PINNs). Specifically, a simple but realistic numerical case study of an extended Jeffcott rotor model, encompassing damping effects and anisotropic supports for a more comprehensive modelling, is considered. PINNs are used for the estimation of five parameters that characterize the health state of the system. These parameters encompass the radial and angular position of the static unbalance due to the disk installed on the shaft, the stiffness along the principal axes of elasticity, and the non-rotating damping coefficient. The estimation is conducted solely by exploiting the displacement signals from the centre of the disk and, to showcase the efficacy and precision provided by this novel methodology, various scenarios involving different constant rotational speeds are examined. Additionally, the impact of noisy input data is also taken into account within the analysis and the performance is compared to that of traditional optimization algorithms used for parameters estimation.

The early diagnosis of cracks in aeronautical structures is a fundamental task for the safe system operation and the optimization of maintenance policies, in view of the increasing interest in life extension programs of several high-investment industries. In principle, these tasks could be fulfilled within a condition-based framework, where direct or indirect observations of the degradation evolution are processed, possibly in real time, by proper diagnostic computational tools. In the past, several attempts have been made to build real-time monitoring systems collecting strain signals acquired from sensor networks. However, in real applications, some issues remain unresolved, for example, the large number of observations available to be handled within a unique diagnostic framework, their relationship with the underlying crack size, and their typical large uncertainties. In this paper, we provide a practical solution by innovatively combining a particle filtering-based model identification algorithm with a measurement system exploiting real-time observations of the crack length reconstructed by a committee of artificial neural networks. The artificial neural networks are trained by simulated strain fields generated by a finite element model. The resulting tool allows to perform an automatic, simultaneous, and real-time (a) selection of the model more properly describing the system state evolution, so as to detect the crack propagation onset time, (b) estimation of the model parameters, and (c) estimation of the crack length, within a unique probabilistic framework based on particle filtering. The methodology is demonstrated with reference to a real helicopter panel subject to fatigue and equipped with a fiber Bragg grating sensor network.