A surrogate assisted adaptive framework for robust topology optimization

This paper presents a novel approach for robust topology optimization (RTO). The proposed approach integrates the hybrid polynomial correlated function expansion (H-PCFE) with the deterministic topology optimization (DTO) algorithm, where H-PCFE is used for computing the moments associated with the objective function in robust design optimization (RDO). It is argued that re-training the H-PCFE model at every iteration will make the overall algorithm computationally expensive and time-consuming. To alleviate this issue, an adaptive algorithm is proposed that automatically decides whether to retrain the H-PCFE model or to use the available H-PCFE model. Since RTO involves a large number of design variables, we also argue that, from a computational point of view, gradient-based optimization algorithms are better suited over gradient-free optimization techniques. However, the bottleneck of using gradient-based optimization algorithms is associated with the computation of the gradients. To address this issue, we propose a procedure for computing the gradients of the objective function in RTO. The proposed approach is highly flexible and can be integrated with the already available DTO codes from literature. To illustrate the performance of the proposed approach, three well-known benchmark problems have been solved; two of them being on the 2D MBB beam and one more on a 3D cantilever beam. As compared to the results of the DTO, RTO yields conservative results which are visible from the additional limbs appearing in the optimized topology of the structure. Furthermore, to justify the use of H-PCFE as a surrogate within the proposed framework, a comparative assessment of the proposed approach against the popular surrogate models has also been presented. It is observed that H-PCFE outperforms other popular surrogate models such as Kriging, radial basis function and polynomial chaos expansion, in both accuracy and efficiency.