Resumen
The emerging Local Maximum-Entropy (LME) approximation, which combines the advantages of global and local approximations, has an unsolved issue wherein it cannot adaptively change the morphology of the basis function according to the local characteristics of the sample, which greatly limits its highly nonlinear approximation ability. In this research, a novel Adaptive Local Maximum-Entropy Surrogate Model (ALMESM) is proposed by constructing an algorithm that adaptively changes the LME basis function and introduces Particle Swarm Optimization to ensure the optimality of the adaptively changed basis function. The performance of the ALMESM is systematically investigated by comparison with the LME approximation, a Radial basis function, and the Kriging model in two explicit highly nonlinear mathematical functions. The results show that the ALMESM has the highest accuracy and stability of all the compared models. The ALMESM is further validated by a highly nonlinear engineering case, consisting of a turbine disk reliability analysis under geometrical uncertainty, and achieves a desirable result. Compared with the direct Monte Carlo method, the relative error of the ALMESM is less than 1%, which indicates that the ALMESM has considerable potential for highly nonlinear problems and structural reliability analysis.