Physics-informed neural network modeling approach for mistuned bladed disks

Due to the demand for lighter aircraft and increased engine efficiency, bladed disks manufactured as a single component (i.e., blisks) have seen increased interest for use in modern turbomachinery, particularly in aerospace applications. However, due to a lack of friction interfaces like those present in bladed disks with inserted blades, blisks contain low intrinsic damping leading to increased vibration amplitudes and stress concentrations in operation. Stress concentrations are further exacerbated due to energy localization from inherent random variations in material properties and geometry, known as mistuning. As such, modeling mistuned blisk dynamics is of utmost importance for blisk design and maintaining structural integrity in harsh operating conditions. Due to the high dimensionality of finite-element blisk models particularly in industry settings, reduced-order models are often necessary to simulate mistuned blisk dynamics with computational efficiency. Reduced-order modeling of blisks has recently been dominated by purely physics-based methods. However, with the increase in experimental data availability and improved computational resources, data-driven methods have seen increased interest. Recently, the authors developed a data-driven approach to model mistuned blisk dynamics with traveling-wave excitation similar to that experienced in operation. This approach was expanded to maintain analytically derived linear and nonlinear relationships via a single physics-informed neural network while maintaining a sector-level viewpoint. Because physical response data from blades is used directly, unlike previous physics-based methods this approach can easily incorporate experimental data such as data measured in bench or operating conditions such as with blade tip timing. Previously, this approach was validated only considering an isolated first mode family with excitations targeting blade-dominated modes. Here, we illustrate the application of this method for a veering region in which multiple disk and blade-dominated modes participate from higher mode families including both bending and torsional modes. Additional considerations for practical application of this approach are discussed, along with further studies to illustrate robustness and generalizability. Validation is shown using a high-fidelity finite-element blisk model considering traveling-wave excitations targeting higher blade and disk-dominated modes in a veering region. For the veering region considered, physical response data from as few as two degrees of freedom per blade tip are needed to achieve high prediction accuracy for test mistuning patterns not used for model training.