Purpose <p>Recent progress in aero-engine technologies has led to the widespread adoption of Nickel-based Single Crystal (SC) blades in turbine blade design. Firstly, this study explores the influence law of crystal orientation on the nonlinear dynamics of the nickel-based single-crystal shrouded bladed disk. Secondly, the research pays attention to the intricate changes in resonance amplitude corresponding to different crystal orientation angles. Ultimately, the surrogate models with different excitation forces are presented to achieve accurate prediction of the nonlinear dynamic response for a single-crystal bladed disk with arbitrary crystal orientations.</p> Methods <p>An innovative approach has been proposed for predicting the nonlinear dynamics of the single crystal shrouded bladed disk. The method employs the multi-harmonic balance method to compute the nonlinear dynamics of the single-crystal shrouded bladed disk. Furthermore, dynamic response prediction method based on Kriging method is implemented to develop the surrogate models, which can predicts the nonlinear dynamics of the single crystal bladed disks under arbitrary crystal orientation accurately.</p> Results <p>Firstly, the numerical simulation indicates that the angles of crystal orientation play important roles in the nonlinear dynamics of the single crystal shrouded bladed disk. Then the surrogate model is constructed on the basis of the numerical results. Finally, the reliability of the surrogate models has been confirmed through various samples. The calculation results show that the effect of crystal orientation on nonlinear dynamic properties for single crystal bladed disk should be considered during the casting process.</p> Conclusions <p>In this research, the significant influence of crystal orientation on the nonlinear behaviors of the single crystal shrouded bladed disk is analyzed. The primary objective of this work is to investigate the effect of the crystal orientations on the nonlinear responses and predict the responses amplitude for different crystal orientations. Unlike previous studies that have primarily focused on strength of single-crystal blades or bladed disks, this paper provides a comprehensive exploration of the nonlinear dynamic properties and the advanced predictive methodologies of tuned bladed disks under arbitrary crystal orientations. The results show that the effect of crystal orientation on the nonlinear response amplitude should be considered when casting the bladed disk to avoid high cycle fatigue.</p>