Nonlinear dynamic prediction and design optimization of bladed-disk based on hybrid deep neural network

In order to overcome the low efficiency of nonlinear dynamic solution, a hybrid deep neural network (HDNN) is constructed based on the integrated deep learning networks for both anticipating nonlinear dynamics as well as evaluating the damping performance of the bladed-disk system in the study. Different physical models are established respectively to characterize the vibratory characteristics and nonlinear solution method is adopted to obtain the true dynamics for surrogate model construction. The results show that HDNN can realize the dynamic prediction with accuracy compared with true numerical solutions under different contact design parameters. The further findings in the case of lumped parameter modeling indicate that high prediction accuracy and good training performance can be obtained by the proposed HDNN when the training size is 0.6 in contrast to the traditional machine learning techniques. The average dynamic prediction error of amplitude and velocity are less than 0.5% and 1.5% respectively, and the average level of damping performance error is almost zero. The training loss can be reduced to 10−4 orders of magnitude to realize the good convergence, and only the cost within 5 ms is required to accomplish the prediction. Furthermore, HDNN-based multi-objective design optimization is conducted to by three different algorithms to obtain the Pareto solution and identify the optimal design parameters. The results exhibit that the NSGA-II outperforms the other two algorithms in capturing the Pareto front solutions. And the dynamic predictions are discussed with different optimal candidates obtained by NSGA-II. The proposed HDNN can meet the demand of accurate dynamic and performance prediction as well as efficient design optimization, providing the analytical support for preliminary turbine design in engineering scenarios.