An adaptive SVD-Krylov reduced order model for surrogate based structural shape optimization through isogeometric boundary element method.

This work presents an adaptive Singular Value Decomposition (SVD)-Krylov reduced order model to solve structural optimization problems. By utilizing the SVD, it is shown that the solution space of a structural optimization problem can be decomposed into a geometry subspace and a design subspace. Any structural response of a specific configuration in the optimization problem is then obtained through a linear combination of the geometry and design subspaces. This indicates that in solving for the structural response, a Krylov based iterative solver could be augmented by using the geometry subspace to accelerate its convergence. Unlike conventional surrogate based optimization schemes in which the approximate model is constructed only through the maximum value of each structural response, the design subspace can here be approximated by a set of surrogate models. This provides a compressed expression of the system information which will considerably reduce the computational resources required in sample training for the structural analysis prediction. Further, an adaptive optimization strategy is studied to balance the optimal performance and the computational efficiency. In order to give a higher fidelity geometric description, to avoid re-meshing and to improve the convergence properties of the solution, the Isogeometric Boundary Element Method (IGABEM) is used to perform the stress analysis at each stage in the process. We report on the benchmarking of the proposed method through two test models, and apply the method to practical engineering optimization problems. Numerical examples show the performance gains that are achievable in comparison to most existing meta-heuristic methods, and demonstrate that solution accuracy is not affected by the model order reduction