Federated learning enables industrial operators to train shared intrusion detection models without disclosing proprietary operational telemetry. However, existing defences operate strictly in update space, leaving aggregators blind to data poisoning; model updates derived from fabricated telemetry remain indistinguishable from honest contributions. We repurpose process invariants, physical relations that always hold in normal operation, such as the conservation of mass, from runtime detection heuristics into a verifiable admission requirement for federated updates, mined automatically from clean operational data. We evaluate this admission gate across two physical water testbeds (SWaT and WADI) and a distribution benchmark (BATADAL), testing seven aggregation rules against telemetry fabrication, exposure-only replay poisoning, and an invariant-aware adaptive adversary. Across three testbeds, the mined invariants reject none of 25 honest shards except every cross-channel fabrication on SWaT and BATADAL, including optimised perturbations that the similarity-based FoolsGold admits in full. On real telemetry, five mined invariants detect 12 of SWaT’s 35 attacks, while nine invariants detect 20. With nine invariants, the admission gate removes 78% of the targeted-attack recall lost to replay poisoning (95% CI 57–97%, $p<0.001$ over 20 seeds) across five standard aggregators and 82% under FedAvg. To reconcile physical admission control with federated data privacy, we show invariant compliance using zero-knowledge proofs (zk-SNARKs) to allow clients to prove batch adherence without revealing operational telemetry.

In this study, we propose a general mathematical modelling framework based on the characteristics of elite athletes’ movements in the touch rugby matches to investigate the dynamic relationship between physical workload and injury risk over time. Our framework extends the Cox-based model in the context of touch rugby by incorporating a time-scaling component and cluster-specific heterogeneity simultaneously. In addition, we allow for the inclusion of covariates (e.g., velocity variation) to capture their effects. We applied our model to high-frequency wearable sensor data collected from 27 elite athletes (15 men and 12 women). The empirical study results show that our model, time-scaled frailty model (TSFM), demonstrates better goodness-of-fit than traditional frailty and Andersen–Gill models. The results reveal that higher velocity variation, particularly during high-intensity phases, and longer time of continuous exposure to the workload spike state significantly increased overload risk, ultimately resulting in injury. It also highlights the importance of individual differences, even under the same exercise intensity. These insights provide coaches with an evidence-based framework for athlete monitoring, allowing for more personalized training loads, tactical deployment, and injury prevention strategies in elite touch rugby environments.