Physics-Informed Neural Network Surrogate Model for Small-Sample Mistuned Bladed Disk

Mistuning in bladed disk structures disrupts their cyclic symmetry, potentially resulting in high cycle fatigue. The stochastic nature of mistuning greatly increases the computational cost of related studies. To improve computational efficiency, previous research has primarily focused on reduced-order models based on finite element methods, whereas the increasing demand for rapid computation and precise predictions has led to the emergence of data-driven approaches. These methods directly use vibration data from bladed disks, eliminating the need for building complex physical models. The accuracy of these methods is dependent on the size of the data, which, however, are often difficult to obtain. To overcome the challenge of insufficient data, this study introduces a Physics-Informed Neural Network Surrogate Model for Small-Sample Mistuned Bladed Disk (PINN-SMBD). This new method combines neural networks with the knowledge of bladed disk dynamics mainly reflected in the following three features: the integration of the governing equations of a mistuned bladed disk in the network architecture, the selection of the input and output according to the frequency independence of the response, and the data augmentation using the cyclic characteristic of bladed disks. Moreover, a dataset construction strategy is proposed that the use of datasets with high variance of mistuning can speed up model convergence and improve accuracy. Finally, a PINN-SMBD model for a dummy bladed disk is built by using only 30 samples which demonstrates remarkable accuracy.