GA-AFedOD: gradient-aligned active federated learning for resource-aware object detection in edge industrial IoT

Visual object detection is essential for defect inspection and process monitoring in edge-deployed Industrial Internet of Things (IIoT). Yet, training accurate detectors across distributed factories faces stringent constraints on data privacy, annotation budgets, and uplink communication. Standard federated learning (FL) preserves locality but often wastes labeling resources on redundant frames and overlooks detection-specific gradient alignment when scheduling clients. To bridge this gap, we propose Gradient-Aligned Active Federated Object Detection (GA-AFedOD), a unified framework that jointly optimizes annotation selection, client participation, and model aggregation as a constrained stochastic program. A novel utility metric integrates box-level uncertainty, prototype diversity, gradient alignment, and resource pricing, enabling edge clients to perform locally guided active querying while the server solves a lightweight primal-dual problem for budget-aware client scheduling. We prove a submodular approximation guarantee for the greedy sampling rule and establish a non-convex convergence bound that explicitly captures the impact of label budgets, client drift, and compression noise. This article further clarifies the relationship with recent federated active learning and industrial detection studies, adds parameter and theory-diagnostic analyses, and distinguishes controlled simulation evidence from real-world deployment validation on industrial datasets such as RasPiDets, Electric Power Fitting Dataset (EPFD), and Diverse Insulator Dataset (DINS). Controlled simulation results show that GA-AFedOD achieves considerably higher mean average precision (mAP) while reducing both annotation costs and uplink consumption by over 40% compared with competitive baselines.