TY - JOUR
T1 - Design sensitivity analysis with polynomial chaos for robust optimization
AU - Ren, Chengkun
AU - Xiong, Fenfen
AU - Mo, Bo
AU - Chawdhury, Anik
AU - Wang, Fenggang
N1 - Publisher Copyright:
© 2020, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2021/1
Y1 - 2021/1
N2 - Polynomial chaos (PC) methods with Gauss-type quadrature formulae have been widely applied for robust design optimization. During the robust optimization, gradient-based optimization algorithms are commonly employed, where the sensitivities of the mean and variance of the output response with respect to design variables are calculated. For robust optimization with computationally expensive response functions, although the PC method can significantly reduce the computational cost, the direct application of the classical finite difference method for the analysis of the design sensitivity is impractical with a limited computational budget. Therefore, in this paper, a semi-analytical design sensitivity analysis method based on the PC method is proposed, in which the sensitivity is directly derived based on the Gauss-type quadrature formula without additional function evaluations. Comparative studies conducted on several mathematical examples and an aerodynamic robust optimization problem revealed that the proposed method can reduce the computational cost of robust optimization to a certain extent with comparable accuracy compared with the finite difference-based PC method.
AB - Polynomial chaos (PC) methods with Gauss-type quadrature formulae have been widely applied for robust design optimization. During the robust optimization, gradient-based optimization algorithms are commonly employed, where the sensitivities of the mean and variance of the output response with respect to design variables are calculated. For robust optimization with computationally expensive response functions, although the PC method can significantly reduce the computational cost, the direct application of the classical finite difference method for the analysis of the design sensitivity is impractical with a limited computational budget. Therefore, in this paper, a semi-analytical design sensitivity analysis method based on the PC method is proposed, in which the sensitivity is directly derived based on the Gauss-type quadrature formula without additional function evaluations. Comparative studies conducted on several mathematical examples and an aerodynamic robust optimization problem revealed that the proposed method can reduce the computational cost of robust optimization to a certain extent with comparable accuracy compared with the finite difference-based PC method.
KW - Design sensitivity
KW - Gauss-type quadrature
KW - Polynomial chaos
KW - Robust design optimization
UR - http://www.scopus.com/inward/record.url?scp=85090777245&partnerID=8YFLogxK
U2 - 10.1007/s00158-020-02704-2
DO - 10.1007/s00158-020-02704-2
M3 - Article
AN - SCOPUS:85090777245
SN - 1615-147X
VL - 63
SP - 357
EP - 373
JO - Structural and Multidisciplinary Optimization
JF - Structural and Multidisciplinary Optimization
IS - 1
ER -