Replica-exchange Bayesian mixture regression reveals cluster-dependent XRD descriptors of tensile modulus in recycled polypropylene

Recycled polypropylene (rPP) exhibits large property variability due to mixed origins and degradation histories, complicating nondestructive grading. In this study, we propose an interpretable Bayesian framework that links X-ray diffraction (XRD) peak features to tensile modulus for virgin/recycled PP blends subjected to xenon-arc weathering. XRD profiles were analyzed by Bayesian peak deconvolution, extracting physically interpretable descriptors from four low-angle crystalline peaks (α(110), α(040), α(130), β(300)) and a broad amorphous halo, yielding 21 explanatory variables per sample. A Bayesian finite mixture of linear regressions with probabilistic feature selection was fitted and posterior inference using replica-exchange Monte Carlo was performed to explore a highly multimodal posterior. The model selected two clusters and achieved an in-sample fit (R2 = 0.81, RMSE = 145 MPa). Replicate-holdout group k-fold cross-validation provided a conservative generalization estimate at the tensile level (R2 = 0.15, RMSE = 320 MPa, N = 120), providing a conservative lower-bound estimate due to specimen mismatch and repeated labels at 0 cycles. Clusters differed in the β(300) descriptor space, and direct comparison of cluster-specific posterior coefficient distributions indicated that the β(300) peak position provided the clearest evidence of cluster-dependent regression behavior, whereas peak broadening was relevant in both clusters. These results suggest that β(300)-related descriptors – potentially reflecting β-phase lattice strain or local disorder – may contribute to modulus beyond β fraction alone. This framework provides interpretable XRD descriptors and uncertainty-aware modulus estimates for grading heterogeneous rPP.