  Remote monitoring systems analyze the environment dynamics in different smart
industrial applications, such as occupational health and safety, and
environmental monitoring. Specifically, in industrial Internet of Things (IoT)
systems, the huge number of devices and the expected performance put pressure
on resources, such as computational, network, and device energy. Distributed
training of Machine and Deep Learning (ML/DL) models for intelligent industrial
IoT applications is very challenging for resource limited devices over
heterogeneous wireless networks (HetNets). Hierarchical Federated Learning
(HFL) performs training at multiple layers offloading the tasks to nearby
Multi-Access Edge Computing (MEC) units. In this paper, we propose a novel
energy-efficient HFL framework enabled by Wireless Energy Transfer (WET) and
designed for heterogeneous networks with massive Multiple-Input Multiple-Output
(MIMO) wireless backhaul. Our energy-efficiency approach is formulated as a
Mixed-Integer Non-Linear Programming (MINLP) problem, where we optimize the HFL
device association and manage the wireless transmitted energy. However due to
its high complexity, we design a Heuristic Resource Management Algorithm,
namely H2RMA, that respects energy, channel quality, and accuracy constraints,
while presenting a low computational complexity. We also improve the energy
consumption of the network using an efficient device scheduling scheme.
Finally, we investigate device mobility and its impact on the HFL performance.
Our extensive experiments confirm the high performance of the proposed resource
management approach in HFL over HetNets, in terms of training loss and grid
energy costs.
