What do we hear from a drum? A data-consistent approach to quantifying irreducible uncertainty on model inputs by extracting information from correlated model output data

In manufacturing processes, controlling system responses with uncertain system inputs, e.g., due to variations in material parameters of critical system sub-components, is a crucial task for performing reliable quality control and verification & validation (V&V) of system design. As a model for a manufacturing process, we consider the production of drums, that is, thin elastic membranes, whose properties are modeled via Dirichlet Laplacian eigenproblems with uncertain diffusion coefficients. Both a quality control and V&V problem are formulated within a data-consistent framework utilizing push-forward and pullback measures. In both problems, the uncertain diffusion coefficients are parameterized for every instance and the corresponding eigen-information defines correlated data streams. Subsequently, the quantities of interest required in the solution to the data-consistent inverse problems are determined by an a posteriori analysis of these data streams using feature extraction techniques. While the methodology proposed here is quite general, the specific efficacy of the proposed methodology is comprehensively explored in the numerical results for both the quality control and V&V problems associated with the manufacturing of drums.