Data-Driven Approach for Predicting Vibration Response of Bladed Disks With Geometric Mistuning

Deviations in the bladed disk manufacturing, such as uneven thickness, surface roughness, or sinkholes in casted wheels, can cause geometric mistuning and result in vibration amplification, severely decreasing reliability. To study the dynamic characteristics of actual industrial bladed disks with complex geometric shapes, it is essential to accurately and quickly forecast the vibration response of geometrically mistuned systems. This remains a challenge because of the high dimensionality of the geometric mistuning parameters and the extreme sensitivity of the vibration response to random geometric mistuning parameters. This paper proposes a deep neural network (DNN) framework for forecasting the vibration response of mistuned blade disks with high-dimensional geometric mistuning parameters. We generated the mistuned parameter matrix to describe the geometric uncertainty by mapping the deviation values of each node in the mistuned blade finite element model. Then, we constructed a geometrically mistuned bladed disk DNN (GMS-DNN) to model the relation between the geometric mistuning parameter matrix and blade vibration response. This approach decouples the mistuned system's vibration equations and substitutes a DNN for the coupling process. The GMS-DNN adopts the transformer encoder to extract geometric mistuning parameter features and uses the blade-disk boundary response to represent the variation of geometric mistuning parameters for different blades to reduce the DNN input parameter dimensions. We verified the validity of the proposed method using geometric deviations from an actual machined industrial-bladed disk. All DNNs in the GMS-DNN exhibited good prediction accuracy on both the training datasets and testing datasets. The results show that the $R2$ value of the predicted response is 0.99 for the unknown test data, while the error of the amplification factor of the actual vibration response is less than 0.01.