Data-Driven Non-Central Wishart Framework for Hybrid Uncertainty Quantification of Aerostructures

This work presents a hybrid uncertainty quantification (UQ) methodology for large-scale structural dynamic systems using a data-informed non-central Wishart distribution to model both parametric variability and model-form uncertainty within a unified random matrix framework. While conventional central Wishart-based random matrix models have demonstrated efficacy in capturing global dispersion in mass, stiffness, and damping matrices, they remain limited by isotropic covariance assumptions and insufficient representation of spatially structured input uncertainties intrinsic to aerospace-grade finite element models. In contrast, the proposed formulation incorporates element-wise statistical descriptors obtained from spatially correlated random field simulations using Karhunen--Lo\`eve (KL) expansion conducted via FEniCSx to calibrate a non-central Wishart distribution. The non-centrality and scale parameters of the Wishart ensemble are inferred to preserve the empirical mean and covariance structure of the system matrices, yielding physically consistent and full-rank stochastic realizations that reflect both aleatoric field-driven perturbations and epistemic modeling imprecision. The method is validated on a clamped rectangular plate, serving as a representative mid-scale aeroelastic subsystem in which reduced-order dynamics, modal coupling, and high-frequency behaviour can be examined rigorously. The evaluation focuses on a reduced non-central Wishart formulation, in which parameter identification is performed in a low-dimensional modal subspace while preserving the empirical statistics of the full system matrices. Comparison with Karhunen--Lo\`eve-based Monte Carlo sampling and central Wishart models demonstrates that the reduced non-central Wishart formulation more accurately captures FRF variability, particularly near densely clustered resonances, while substantially reducing the computational burden associated with full-field stochastic simulation. By embedding high-fidelity simulation-derived statistics into a structured random matrix ensemble, the proposed framework delivers a computationally efficient and physically interpretable alternative to traditional parametric UQ, with direct relevance to large-scale aerostructural models. It is especially suited for frequency-sensitive aerospace structures requiring probabilistic analysis without reliance on exhaustive sampling.