Efficient prediction for time domain responses of forced oscillations and limit cycle oscillations

A nonlinear reduced-order model (ROM) using Kriging surrogate-based recurrence framework (KSBRF) was built. Because Kriging interpolation has the ability of estimating nonlinear input-output relationship, nonlinear aerodynamic forces and characteristics of LCO (limit cycle oscillations) could be estimated with KSBRF ROM. Firstly, the relationship between input and output of a nonlinear system was built using KSBRF ROM. Then, the identification of nonlinear unsteady aerodynamic forces was conducted when an airfoil had pitch/plunge oscillations. It was shown that under the same free-stream's Mach number, the prediction results with KSBRF ROM agree well with those with CFD, the mean prediction errors of drag coefficient and pitch moment coefficient are within 2.0%; considering a variable free-stream Mach number, the mean prediction errors of lift coefficient and pitch moment coefficient are within 2.5%, the preceding error of drag coefficient is less than 7%; it is concluded that considering the history effect is helpful to improve the accuracy of ROM through studying the effects of different m, n values on the accuracy of ROM; the LCO characteristics of NACA64A010 airfoil are predicted with the nonlinear ROM, the prediction results with KSBRF ROM agree well with those with CFD, the errors are less than 5.17%.