Tensor product fusion of LIBS and acoustic emission signals for waste identification in recycling

Accurate identification of recyclable waste is essential for efficient material recovery. However, existing spectroscopic studies have not fully addressed the combined challenges of integrating hierarchical identification requirements, representing subtle spectral differences, and effectively exploiting cross-modal complementarity. To address these gaps, this study develops a two-stage classification framework for recyclable waste, integrating laser-induced breakdown spectroscopy (LIBS) and plasma acoustic emission signals (PAES). For coarse classification, a Difference–Summation Gramian Angular Field (DSGAF) encoding method transforms one-dimensional LIBS spectra into two-dimensional representations to enhance spectral discriminability. For fine subclassification, LIBS-derived elemental-composition information is combined with complementary physical-response information carried by PAES. Mutual information (MI) and Pearson correlation coefficient (PCC) are used for feature selection, and a LIBS–PAES Tensor Product Enhancement (LPTE) method is introduced to explicitly exploit cross-modal interactions. The DSGAF-based 2DCNN increased the independent-test accuracy from 91.11% to 98.48% for classifying recyclable waste into paper–wood, glass, plastic, metal, and textile categories. For fine subclassification of plastic, metal, and textile waste, the MI_LPTE model achieved accuracies above 99% and outperformed unimodal and conventional fusion models. These results demonstrate the potential of hierarchical LIBS–PAES sensing for recyclable-waste sorting and material recovery.