A Probabilistic Framework for Effective Wall Width Estimation in Wire Arc Additive Manufacturing

Abstract

Wire Arc Additive Manufacturing (WAAM) is a layer-by-layer metal additive manufacturing process that uses wire feedstock and an electric arc to build metallic components. Accurate estimation of Effective Wall Width (EWW) is important for dimensional consistency and structural integrity. This work contributes a probabilistic uncertainty-quantification framework for estimating EWW in WAAM under uncertain process inputs. The framework combines literature-based thermophysical and geometric relations to express EWW as a function of key process parameters, including heat input, wire feed speed, travel speed, and wire cross-sectional area. For Ti-6Al-4V deposition, the uncertain inputs were modeled as independent Gaussian random variables with a coefficient of variation of 15%. Monte Carlo Simulation was first used to propagate input uncertainty, while the unknown layer angle (θ) was estimated for each sample using a nonlinear solver. A lognormal distribution was then fitted to the resulting θ values and incorporated into the computational framework. To improve estimation efficiency, numerical optimization was used to identify the most probable input region contributing to EWW, and Importance Sampling was subsequently applied for variance-reduced estimation. Failure probability was estimated using quantile-based thresholding of the simulated EWW values. Overall, the study establishes a computational foundation for uncertainty-aware assessment of WAAM geometry and provides a basis for future data-informed refinement and validation.