<p>We investigate the spectral fabric of heterogeneous residual stress fields that emerge in stochastic manufacturing processes, using shot peening as a representative test case. Eshelby-like inclusions are employed as a reduced-order basis for stress prediction and compared against high-fidelity finite element simulations. Impact overlap at higher coverages introduces nonlinear interactions that linear superposition fails to capture. To resolve these effects, we introduce a Power Spectral Density Ratio (PSDR) that functions as an interpretive filter, identifying specific frequency bands where physical mechanisms—such as plastic saturation and surface upheaval—deviate from linear assumptions. The PSDR serves as a statistical fabric descriptor, quantifying both long-range coherence and local heterogeneity. This framework provides a scalable route for predicting residual stress evolution while establishing fabric quantification as a transferable paradigm for spatially variable manufacturing states.</p>