Physics-Informed Activity Recognition and Service-Response Analysis for Elderly Care Using a SLEEEP-PIR Sensor Array

Privacy-preserving monitoring and timely service response are central challenges in home-based elderly care. This study presents a physics-informed framework that integrates SLEEEP-PIR signal preprocessing, fall-like candidate generation, four-class ensemble classification, and queueing-based service-response analysis, evaluated on the public PIRvision_FoG_presence_detection release. The activation and amplitude thresholds of the physical rules are formulated on baseline-removed deviation features, which places the 55 channels of the array on a comparable scale. Over ten acquisition-block 80/20 splits, LightGBM reached a weighted F1-score of 0.986 and a macro F1-score of 0.972 for the activity states vacant, stationary, normal movement and large-amplitude movement, and the same feature space supports a wide-coverage low-amplitude pattern that is routed to human verification as a candidate alert rather than an automated decision. The queueing analysis reproduces the analytical M/M/c benchmark and quantifies how staffing and service-time assumptions shape simulated waiting time under explicitly specified scenarios. These results support the methodological feasibility of coupling privacy-preserving activity analysis with service-response modelling.