Physics-Informed Neural Networks for Reduced-Order Modeling of Turbomachinery Blisks With Small and Large Mistuning

Abstract Comprehensively understanding the structural dynamics of turbomachinery blisks is of critical importance to the gas turbine industry. Located in the compressor and turbine stages, vibrations of these structures are amplified by their inherent mistuning present in blisks. Mistuning can be small or large. Small mistuning is defined as inherent deviations from nominal sector properties and geometry that does not significantly change blade-alone mode shapes or frequencies. Large mistuning is described as significant blade variations like those resulting from damage during operation and/or after repairs, such as geometric changes due to foreign object ingestion or blends. Large mistuning significantly changes the blade-alone mode shapes and frequencies, resulting in rogue blades. Mistuning breaks the nominal cyclicity of the system, resulting in shifts in frequency responses and large vibration amplifications. Hence, it is paramount for the safe operation of gas turbines to predict vibration responses of blisks with both small mistuning and rogue blades. Predicting mistuned blisk responses requires a significantly higher computational effort compared to cyclic systems. To address this issue, physics-based and data-driven reduced-order models (ROMs) have been developed. While many physics-based ROMs have been developed for predicting blisk responses with small mistuning, a much smaller number of methods have focused on blisks with both small and large mistuning. The pristine-rogue-interface modal expansion (PRIME) ROM is one of these methods. PRIME is a projection-based ROM where the basis vectors are composed of tuned modes from two cyclic systems: (1) modes of the blisk with all blades pristine (used only for sectors that only have small mistuning), and (2) modes of the blisk with all blades rogue (used only for rogue sectors that have large and possibly small mistuning). While purely physics-based ROMs are accurate, they require large finite element (FE) models to characterize the system dynamics, and cannot be enhanced using experimental data. Thus, this paper proposes a novel physics-informed data-driven approach to compute blisk responses with both large and small mistuning. Similar to a classical physics-based approach (i.e., PRIME), this paper utilizes two physics-informed neural networks to compute the transfer function matrices of two systems: (1) a cyclic pristine blisk with small mistuning, and (2) a cyclic rogue blisk with small mistuning. These transfer functions are then introduced in a linear system of equations to compute the blade root responses of a blisk with small mistuning and rogue blades. Blade tip responses can then be computed using root responses through a third neural network. This proposed method has been tested using a blisk lumped mass model with 18 blades. Results show highly accurate predictions, with absolute errors below 10% for all presented mistuned blisk configurations. Future work focuses on further enhancing the accuracy of this method by enhancing the neural network hyperparameters.