Quantile-based topology optimization under uncertainty using Kriging metamodel

This paper investigates reliability-based topology optimization (RBTO) and proposes a novel quantile-based topology optimization (QBTO) method. With this method, the traditional RBTO model is transformed into an equivalent quantile-based formulation, which can well avoid the issues existing in RBTO with Monte Carlo simulation (MCS), i.e., stagnation of optimizer due to near zero sensitivities of probabilistic constraint with regard to element densities, huge computational cost on calculating sensitivities, and the discontinuity of failure indicator function. Specially, in QBTO, the sensitivities only require to be calculated at the sample corresponding to the quantile instead of all MCS samples, which can drastically reduce the computational effort. Furthermore, a sequential update strategy of Kriging metamodel is developed to efficiently calculate the quantile by evaluating the true constraint at fewer samples, rather than all MCS samples. The high accuracy and efficiency of QBTO are validated by truss, beam and bridge problems. (C) 2022 Elsevier B.V. All rights reserved.