Parameterized coefficient fine-tuning-based polynomial chaos expansion method for sphere-biconic reentry vehicle reliability analysis and design

Polynomial chaos expansion (PCE) is an efficient surrogate modeling method that can be used for reliability analysis. However, the existing methods generally require sufficient labeled data to build a high-precision surrogate model and cannot use much-unlabeled data. Thus, this paper proposes a parameterized coefficient fine-tuning-based PCE (PCFT-PCE) method. Based on limited labeled data, the PCFT-PCE method first uses the traditional PCE method to initialize the parameterized expansion coefficients of a single-layer neural network. Then based on abundant unlabeled data, the single-layer neural network parameters are fine-tuned by adopting two properties of PCE to construct an unsupervised loss function. Based on the PCFT-PCE method, this paper builds a sphere-biconic reentry vehicle reliability-based design optimization (SBRV-RBDO) framework to minimize the mass and the highest temperature considering geometric and material parameters' uncertainties, where a combination penalty method is proposed to adjust and balance the mass and the highest temperature constraints. Finally, a numerical example and an engineering case validate the proposed methods. The results show that the proposed PCFT-PCE method builds a more accurate PCE model with a little extra calculation time. The SBRV-RBDO framework helps engineers to find reliable optimization schemes for SBRV conceptual design.