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.

 

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.

 

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.

 

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.

 

Together, these contributions establish a spectral–mechanical framework that unifies analytical elasticity, experimental metrology, and data-driven modeling under a common statistical language. The 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.