But how can I optimise my high-dimensional problem with only very little data? – A composite manufacturing application

• Published in: International journal of solids and structures 2024-08, Vol.300, p.112941, Article 112941
• Main Authors: Chen, Siyuan, Thompson, Adam J., Dodwell, Tim J., Hallett, Stephen R., Belnoue, Jonathan P.-H.
• Format: Article
• Language: English
• Subjects: Composites forming; Dimension reduction; Gaussian process surrogate model; Real-time optimisation; Sequential design
• ISSN: 0020-7683; 1879-2146
• DOI: 10.1016/j.ijsolstr.2024.112941

•A framework aiming at minimising defects in dry fibre textile forming is proposed.•A kernel-combined Gaussian Process (GP) emulates a Finite Element (FE) model.•Dimension reduction allows decreasing data sparsity issues in high dimension.•Active learning efficiently generates new data points to improve the GP sequentially.•100 expensive FE simulations are sufficient to find a good optimum for an 8D problem. In this research, a Gaussian process (GP) surrogate modelling framework for the forming process of dry carbon-fibre textile was investigated. A particular focus of the work is the development of dimension reduction algorithms, allowing to solve high-dimensional sparse optimisation problems. The concept of active subspace is adopted to find the principal space of the problem. Then, a low-dimensional (i.e., active) subspace can be obtained by selecting the directions with highest explained variance. A kernel-combined GP format is developed. This takes advantage of the active subspace to build a robust, high-dimensional emulator that can be regarded as a special case of multi-fidelity GP. A two-step adaptive sequential design approach is adopted, which further improves the efficiency of data design. Different sequential design strategies are compared. A case study with eight input parameters demonstrates the capability of the proposed approach, where an accurate and robust optimum condition is obtained from only tens of simulations.