Entropy-resolved q-rung orthopair hypergraph diffusion enables robust structural sensor fusion

Abstract Higher-order sensor groups and incomplete reliability evidence are usually modelled separately, preventing unified analysis of topology, ambiguity and adversarial corruption. This study introduces entropy-resolved q-rung orthopair hypergraph diffusion (ER-qROHD). Residual q-power mass and binary entropy define evidence-gated incidences. The resulting transition is row-stochastic, reversible and similar to a positive-semidefinite matrix. An anchored iteration has a unique fixed point, geometric convergence and a strictly convex energy representation. Median-centred clipping yields bounded contamination influence. An operator-specific Green-kernel analysis further partitions source influence, proves distance-decaying locality and certifies perturbations on specified sensor subsets. In a fully specified 12-sensor synthetic computational benchmark with 400 replicates per missingness condition, ER-qROHD achieved the lowest reconstruction error from 0 to 40% missingness. At 20% missingness, RMSE was 0.219 versus 0.288 for crisp diffusion and 0.385 for median-filled observations; the paired crisp reduction was 0.069 (95% interval 0.065–0.073). Ablation attributed the material gain to clipping and evidence-weighted transport; removing residual allocation changed RMSE by only + 0.0001 and removing the entropy penalty by -0.0003, so this benchmark does not identify an independent entropy benefit. A 20-cell stress analysis identified attack multiplicity as the dominant degradation mechanism; at four attacks RMSE rose to 0.2756–0.2831, while q-entropy sensitivity changed RMSE by only 0.30%. Primary benchmark data, numerical results and executable code are included, with an accompanying deterministic script for the added validation. Additional 24- and 48-sensor synthetic tests covered two hypergraph structures, clustered missingness, altered attack magnitude, ambiguity-enriched evidence, and graph-Tikhonov and Huber-graph baselines. The study still uses fixed synthetic topologies and edge weights, random-sign attacks with at most four attacked sensors, and no physical SHM data; the median guarantee requires fewer than half of the observed values to be contaminated, and paired intervals quantify computational replicates rather than population uncertainty.