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 ROMagree 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%.%建立一种基于改进Kriging的KSBRF（Kriging-Surrogate-Based Recurrence Framework）降阶模型（Reduced－Order Model，ROM），用于高效地预测非线性非定常气动力及力矩、极限环振动（Limit Cycle Oscillations，LCO）等。首先基于 Kriging 代理模型建立非线性系统输入－输出关系的循环预测框架。然后对翼型做沉浮／俯仰组合运动时的非线性非定常气动力进行辨识。结果表明：在固定来流马赫数情况下，KSBRF 预测结果与 CFD 计算结果吻合良好，阻力系数及俯仰力矩系数等的平均预测误差均在2．0％以内；在变来流马赫数情况下，升力系数和俯仰力矩系数的平均预测误差在2．5％以内，而阻力系数的预测误差则稍大，但也不超过7．0％。通过研究不同 m，n 取值对模型精度的影响，得出考虑历史效应有利于提高当前时间步的模型预测精度。除此之外，还对 NACA64A010翼型的 LCO 振动形态进行预测，预测结果与CFD 计算结果吻合良好，误差均保证均小于5．17％，节省近三分之二的计算时长。
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