Hierarchical multi-response Gaussian processes for uncertainty analysis with multi-scale composite manufacturing simulation

Variations of constituent fiber and matrix properties and process conditions can cause significant variability in composite parts and affect their performance. The focus of this paper is to establish a new computational framework that can efficiently quantify the uncertainty propagation of parts manufactured through the resin transfer molding (RTM) process. RTM involves a sequence of inter-related processes that span multiple spatial and temporal scales. This calls for a multi-scale analysis for the nominal process, which is computationally complex and intensive. A direct Monte Carlo simulation of uncertainty quantification leads to prohibitive cost. In this research we leverage a sequentially architected multi-response Gaussian process (MRGP) meta-modelling approach to facilitate a hierarchical procedure. This can dramatically reduce the computational cost, and allow us to characterize the process outputs of interest at different scales and at the same time capture the intrinsic correlation amongst these outputs. Moreover, integrating a global sensitivity analysis with the hierarchical MRGP meta-models yields the importance ranking of uncertainty propagation paths. This computational framework provides a quantitative assessment tool of the uncertainties in composite manufacturing. Case study on curing-induced dimensional variability of a curved composite part is conducted for demonstration and validation.