Physics-informed machine learning approach for reduced-order modeling of integrally bladed rotors: Theory and application

Integrally bladed rotors are commonly used in aircraft and rocket turbomachinery and known to exhibit complex dynamics when subject to operational loading conditions. Though nominally cyclic-symmetric structures, in practice, cyclic symmetry is destroyed due to mistuning caused by random sector-to-sector imperfections in material properties and geometry. Simulating mistuned blisk dynamics using high-fidelity models can be computationally expensive, thus, a variety of physics-based reduced-order models have been previously developed. However, these models cannot easily incorporate experimental data nor leverage potential benefits of data-driven and machine-learning-based approaches. Here, we present a novel first-of-its-kind physics-informed machine learning modeling approach that incorporates physical laws directly into a novel network architecture while maintaining a sector-level viewpoint. The approach is combined with an assembly procedure resulting in a significantly smaller linear system based on blade-alone response data, and can directly incorporate physical response data like that measured with blade tip timing and/or traveling-wave excitation. Validation is shown using a large-scale finite-element model, with multiple traveling-wave forced-response predictions and response selection cases considered. Using only as little as a single degree of freedom per sector from the blade tip, this approach shows high accuracy relative to high-fidelity simulations.