Energy-Efficient Hierarchical Federated Anomaly Detection for the Internet of Underwater Things via Selective Cooperative Aggregation

Kenechi Omeke; Michael Mollel; Lei Zhang; Qammer H. Abbasi; Muhammad Ali Imran

cs.LGMar 25, 2026

Energy-Efficient Hierarchical Federated Anomaly Detection for the Internet of Underwater Things via Selective Cooperative Aggregation

Authors: Kenechi Omeke, Michael Mollel, Lei Zhang, Qammer H. Abbasi, Muhammad Ali Imran

Organizations: James Watt School of Engineering, University of Glasgow, U.K.

Abstract

Anomaly detection is a core service in the Internet of Underwater Things, yet training accurate distributed models underwater is difficult because acoustic links are low-bandwidth, energy-intensive, and often unable to support direct sensor-to-surface communication. Standard flat federated learning therefore faces two coupled limitations in underwater deployments: expensive long-range transmissions and reduced participation when only a subset of sensors can reach the gateway. This paper proposes an energy-efficient hierarchical federated learning framework for underwater anomaly detection based on three components: feasibility-aware sensor-to-fog association, compressed model-update transmission, and selective cooperative aggregation among fog nodes. The proposed three-tier architecture localises most communication within short-range clusters while activating fog-to-fog exchange only when smaller clusters can benefit from nearby larger neighbours. A physics-grounded underwater acoustic model is used to evaluate detection quality, communication energy, and network participation jointly. In large synthetic deployments, only about 48% of sensors can directly reach the gateway in the 200-sensor case, whereas hierarchical learning preserves full participation through feasible fog paths. Selective cooperation matches the detection accuracy of always-on inter-fog exchange while reducing its energy by 31-33%, and compressed uploads reduce total energy by 71-95% in matched sensitivity tests. Experiments on three real benchmarks further show that low-overhead hierarchical methods remain competitive in detection quality, while flat federated learning defines the minimum-energy operating point. These results provide practical design guidance for underwater deployments operating under severe acoustic communication constraints.

Figures & tables

Panel of Figure 1 — Fig. 1: Proposed three-tier HFL architecture for IoUT with feasibility-aware association, compressed uplinks, and selective fog cooperation.

Reference	Main contribution	HFL	Energy
McMahan et al. [ 7 ]	FedAvg: communication-efficient distributed learning.		$\sim$
Li et al. [ 23 ]	FedProx: proximal term for heterogeneous FL.
Karimireddy et al. [ 24 ]	SCAFFOLD: variance reduction for client drift.
Liu et al. [ 9 ]	Client-edge-cloud HFL in cellular networks.	✓	$\sim$
Luo et al. [ 10 ]	HFEL: cost-efficient HFL with edge association.	✓	✓
Wang et al. [ 11 ]	Unified clustering for HFL with peer-to-peer exchange.	✓	$\sim$

TABLE I: Representative related works and positioning of this paper. (✓: explicitly addressed;

\sim

: partially/implicitly addressed; blank: not addressed.)

Panel of Figure 3 — Fig. 2: Stratified IoUT system model. Sensors (deep layer) transmit local model updates to fog aggregators (mid-water); fog nodes cooperatively exchange partial aggregates (dashed) and forward to the surface gateway.

Parameter	Meaning	Baseline
$L_{x},\,L_{y}$	Horizontal area	$2000\times 2000$ m
$H$	Max depth	1000 m
$N$	Sensor nodes	100 (varied: 50–200)
$M$	Fog aggregators	10 (varied: 5–20)
$z_{s}^{\min},\,z_{s}^{\max}$	Sensor depth range	500–1000 m
$z_{f}^{\min},\,z_{f}^{\max}$	Fog depth range	100–400 m

TABLE II: Baseline system-model and learning parameters; experiment-specific overrides are stated in Section VI .

Panel of Figure 5 — Fig. 3: Bi-level view of the framework: hierarchical FL training (top) and the decision-rule layer that selects sensor associations and fog cooperation patterns (bottom).

Fig. 4: Convergence behaviour of the synthetic method set used in the main scalability study. (a) Training loss at

N{=}150

. (b) Training loss at

N{=}200

. Across both scales, the loss curves flatten by roughly rounds 10–12, supporting the choice

T{=}20

for the main synthetic experiments. Error bands denote one standard deviation over three seeds.

Fig. 5: Participation and trade-off results in synthetic IoUT deployments. (a) Direct gateway reachability decreases with scale, while fog-assisted reachability remains near-complete. (b) Detection quality as a function of network scale. (c) Per-sensor communication energy as a function of network scale. Error bars denote one standard deviation over three seeds.

$N$	Method	Participation	F1 score	Energy (J)
50	FedProx	0.51	0.8548 $\pm$ 0.0236	4.0 $\pm$ 0.7
	HFL-NoCoop	0.98	0.8481 $\pm$ 0.0075	33.5 $\pm$ 0.1
	HFL-Selective	0.98	0.8478 $\pm$ 0.0078	36.9 $\pm$ 2.4
	HFL-Nearest	0.98	0.8519 $\pm$ 0.0106	58.9 $\pm$ 0.1
100	FedProx	0.49	0.8584 $\pm$ 0.0044	7.7 $\pm$ 1.0
	HFL-NoCoop	0.96	0.8616 $\pm$ 0.0121	67.0 $\pm$ 0.1

TABLE III: Scalability results under acoustic reachability constraints. Gateway reachability falls from 0.51 at

N{=}50

to about 0.48 at

N{\geq}150

, while feasible fog reachability rises from 0.98 at

N{=}50

to essentially full coverage by

N{\geq}150

. Mean

\pm

std over three seeds.

Fig. 6: Engineering effects of selective cooperation and compressed uploads. (a) Total energy of hierarchical methods at

N{=}150

and

N{=}200

; the annotated F1-score values show that selective cooperation retains the accuracy of always-on cooperation while substantially reducing its cost. (b) Compression savings in matched low-vs-full upload tests. Error bars denote one standard deviation over three seeds where applicable.

Fig. 7: Non-IID sensitivity study at

N{=}100

M{=}10

, and

T{=}20

. (a) F1 score under strongly non-IID and near-IID partitions. (b) Total communication energy. FedProx is strongest at

\alpha{=}0.1

in this setting, but HFL-Selective remains close to the other hierarchical variants while using substantially less energy than HFL-Nearest. Error bars denote one standard deviation over three seeds.

Method	SMD PA-F1	SMD E (J)	SMAP PA-F1	SMAP E (J)	MSL PA-F1	MSL E (J)
Centralised	0.7223 $\pm$ 0.0168	1417.5 $\pm$ 2.9	0.7181 $\pm$ 0.0047	543.0 $\pm$ 1.4	0.8827 $\pm$ 0.0056	493.6 $\pm$ 1.4
FedAvg	0.7930 $\pm$ 0.0130	13.3 $\pm$ 1.6	0.7152 $\pm$ 0.0068	5.4 $\pm$ 1.1	0.8738 $\pm$ 0.0015	5.8 $\pm$ 1.5
FedProx	0.7937 $\pm$ 0.0119	13.3 $\pm$ 1.6	0.7197 $\pm$ 0.0106	5.4 $\pm$ 1.1	0.8738 $\pm$ 0.0015	5.8 $\pm$ 1.5
HFL-NoCoop	0.8013 $\pm$ 0.0095	115.0 $\pm$ 0.2	0.7233 $\pm$ 0.0062	42.9 $\pm$ 0.1	0.8727 $\pm$ 0.0014	34.5 $\pm$ 0.2
HFL-Selective	0.8015 $\pm$ 0.0097	135.2 $\pm$ 8.1	0.7236 $\pm$ 0.0067	51.3 $\pm$ 3.0	0.8727 $\pm$ 0.0014	38.5 $\pm$ 5.6
HFL-Nearest	0.8032 $\pm$ 0.0095	201.7 $\pm$ 0.2	0.7183 $\pm$ 0.0037	74.6 $\pm$ 0.2	0.8727 $\pm$ 0.0014	59.2 $\pm$ 0.9

TABLE IV: Real-benchmark results over three seeds; performance is reported as PA-F1.

Fig. 8: Grouped comparison across the SMD, SMAP, and MSL benchmarks. (a) PA-F1 by method and dataset. (b) Total communication energy on a logarithmic scale. The figure makes the main real-data pattern visually explicit: flat FL offers the lowest-energy operating point, while low-overhead hierarchical methods remain competitive in detection quality and always-on cooperation is consistently the costliest hierarchical option. Error bars denote one standard deviation over three seeds.

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Federated Low-Rank Koopman Learning for Multivariate Time-Series Anomaly Detection in IoT Systems

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Koopman Operator Learning Edge ML Time-Series Anomaly Detection Anomaly Detection

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Distributed IoT systems generate multivariate time-series streams for monitoring physical assets, servers, and embedded sensing platforms. Detecting abnormal temporal behavior is critical for fault diagnosis, predictive maintenance, and security. However, practical IoT anomaly detection is hindered by decentralized and non-IID data, limited bandwidth, and the constrained computation and memory of edge devices. This paper proposes FedKAD, a resource-efficient federated Koopman anomaly detection framework for distributed IoT multivariate time series. Unlike deep-learning-based anomaly detectors that require training and communicating large neural models, FedKAD learns normal temporal dynamics through lightweight sliding-window Koopman representations. Federated training is formulated as a low-rank consensus problem, where raw sensor streams and local reduced dynamics remain on device while only compact subspace variables are exchanged with the server. To optimize the shared representation under orthonormality constraints, we develop a federated Stiefel-ADMM algorithm and provide convergence and stationarity analysis under partial client participation. During inference, each client detects anomalies locally by measuring the prediction residual between observed future trajectories and the learned Koopman dynamics. Experiments on four widely used multivariate time-series anomaly detection benchmarks show that FedKAD maintains or improves detection performance compared with federated deep-learning baselines. More importantly for IoT deployment, FedKAD provides up to

2.1\times10^3

faster training,

80\times

lower communication, and

79\times

lower inference latency than neural baselines, confirming its suitability for resource-constrained edge devices.

Abstract

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