Spectral Characterization and Reduced-Order Modeling of Industrial Shot Peening

<p dir="ltr">We develop a unified framework for understanding and predicting the heterogeneous residual stress fields that emerge from stochastic surface processes, with shot peening serving as a representative system. Although peening has long been recognized for its ability to enhance fatigue performance through near-surface compressive stresses, the underlying stress fields are spatially complex---shaped by random impact sequences, evolving media morphology, and nonlinear material response.</p><p dir="ltr">The spectral fabric of residual stress fields is investigated using Eshelby-like inclusions as a reduced-order mechanical basis. Finite element simulations reveal nonlinear overlap effects at increasing impact coverage, which are captured through a power spectral density ratio (PSDR) filter. The PSDR not only reconciles analytical and numerical models but also serves as a statistical descriptor of long-range coherence and local heterogeneity in stochastic stress fields.</p><p dir="ltr">High-resolution optical profilometry of peened Almen strips is used to extract three-dimensional surface topographies, from which spatial power spectral densities (PSDs) are computed. These spectra exhibit frequency-dependent amplification and systematic peak shifts with increasing impact velocity and coverage. A normalized PSD metric isolates the most process-sensitive frequency bands, demonstrating that spectral descriptors capture physically meaningful structure beyond conventional scalar roughness parameters.</p><p dir="ltr">These insights are integrated into a neural network enabled flowsheet for shot peening. A three-mode degradation model tracks the evolution of media size and shape under repeated recirculation, while a convolutional long short-term memory (ConvLSTM) neural network--trained on finite element data--predicts the evolving residual stress field in real time. This hybrid model enables mechanistically grounded, data-efficient prediction of process outcomes under realistic industrial conditions.</p><p dir="ltr">Together, these contributions link analytical elasticity theory, experimental metrology, and data-driven process modeling using statistical frameworks. This approach emphasizes interpretability, showing that even highly stochastic surface processes can be described through reproducible spectral metrics and reduced-order physical models. In doing so, the work provides a transferable foundation for modeling and monitoring surface treatments where spatial heterogeneity governs performance.</p>