Session: 28-01: Reduced-Order Modeling of bladed disks

Paper Number: 152603

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

Comprehensively understanding the structural dynamics of turbomachinery blisks is of critical importance to the gas turbine industry. Located in the compressor and turbine stages, blisks operate in extreme conditions being exposed to high aerodynamic forces and temperatures. Additionally, due to their low damping, they vibrate at high amplitudes, making them susceptible to high-cycle fatigue, which can have dangerous effects during operation. Furthermore, vibrations are amplified by the inherent mistuning present in blisks. Mistuning can be small or large. Small mistuning is due to small deviations from the nominal sector properties. Small mistuning does not significantly change blade-alone mode shapes or frequencies. Large mistuning is due to significant blade damage during operation or repairs, such as geometric changes due to blends or foreign object ingestion, resulting in rogue blades. Large mistuning changes significantly the blade-alone mode shapes and frequencies. Mistuning breaks the 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. Most physics-based techniques focus on predicting blisk responses with small mistuning. In those methods, mistuning is characterized as small deviations in the cantilever blade frequencies with no blade-alone mode shape variation. Early such methods are based on component mode synthesis (CMS), conceptually dividing the blisk into two components, the disk and the blades, and computing modes of each component and interface constraint modes to form a ROM. Furthermore, to reduce the ROM size and increase computational efficiency other state-of-the-art methods use modes of the nominal cyclic symmetric system within a frequency range of interest to form ROMs by projection of the blisk equations of motion.

A much smaller number of methods focused on blisks with both small and large mistuning. The pristine-rogue-interface modal expansion (PRIME) is one of these methods. PRIME forms projection-based ROMs where the basis vectors are composed of modes of two tuned modes from two cyclic systems: 1) modes of the blisk with all blades pristine used only for the sectors that have only small mistuning, and 2) modes of the blisk with all blades rogue used only for the rogue sectors that have both small and large mistuning.

Nevertheless, while all physics-based ROMs are very accurate, they require large finite element (FE) models to characterize the system dynamics, and they cannot be enhanced using experimental data. Thus, data-driven techniques have been developed recently. One of the most advanced data-driven approach utilizes a neural network to predict transfer functions for a blade i as a function of the motion all the other blades j≠i and the forcing on blade i. The loss function for training this network encodes the equations of motion of the blisk. Yet, while this physics-informed approach provides accurate predictions, this approach cannot be extended to blisks with large mistuning.

Thus, this paper proposes a novel physics-informed data-driven approach to compute blisk responses with both large and small mistuning. Similar to the classical approach in 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 9% for all presented mistuned blisk configurations. Future work focuses on further enhancing the accuracy of this method by enhancing the neural-network hyperparameters.

Presenting Author: Mihai Cimpuieru University of Michigan - Ann Arbor

Presenting Author Biography: Mihai Cimpuieru is a PhD candidate at University of Michigan performing research in structural dynamics using data-driven and physics based techniques in Professor Bogdan Epureanu's lab. Currently, he is working on methods to predict blade vibrations in blisks using physics-informed neural networks. He has worked on mistuning ID methods for turbomachinery components, on the development of friction & impact enhanced vibration absorbers, and on system parameter ID using experimental approaches.

Authors:

Mihai Cimpuieru University of Michigan - Ann Arbor
Sean Kelly University of Michigan - Ann Arbor
Bogdan Epureanu University of Michigan - Ann Arbor