Effective anomaly detection frameworks are a central pillar of the Industry 4.0 paradigm. In this paper, we introduce an Optimal Transport (OT)-based framework for anomaly detection, designed to detect deviations from normal behaviour in time-series sensor data. The OT-based method requires minimal user input and adapts to real-time data without the need for labelled training data. Our method effectively addresses existing limitations related to data labelling, generalisability, and scalability, demonstrating resilience against short-term fluctuations, noise, and data gaps — common challenges in industrial environments. Additionally, our method provides counterfactual explanations improving the auditability of the approach when deployed in industrial settingsThe proposed method learns the mapping between normal and observed operating conditions through a sliding reference window that adapts to the dynamicity of the data. We evaluate our approach on three industrial datasets, from shipping, industrial HVAC systems, and publicly available benchmark data. The method was highly effective in identifying anomalies and reducing false positives, outperforming traditional methods, while maintaining computational efficiency and ease of configuration.

The recent advances in Graph Neural Networks (GNN) are poised to improve machine learning of IoT systems at the edge. Particularly, GNNs allow modeling the topology of distributed systems, including their physical laws, from sensors data. However, one of the main limitations of using GNNs arises from their adjacency matrix. The adjacency matrix of GNNs needs to be defined a priori and represents the connectivity between the edges of a network. Usually, the adjacency matrix of GNNs consists of binary values that are equal to 1 when two edges are physically connected and 0 otherwise. This representation considers connectivity in terms of proximity and assumes that they are of equal significance. However, in certain applications, areas that are not physically connected can share more properties than physically connected areas. This necessitates new methods for devising the adjacency matrix and leads us to propose an efficient approach for determining the adjacency matrix of GNNs. Our approach extends GNNs in two ways. First, we employ a mechanism that utilizes the time series data at the edges to determine the eigenvalues and eigenvectors associated with each edge, allowing us to compute the proportion of variance. Subsequently, we use the proportion of variance to construct our adjacency matrix. Second, we utilize Dynamic Time Warping (DTW) to cluster related time series at the edge and construct our adjacency matrix. We then integrate the newly derived adjacency matrix into the GNN operating with a sequence to sequence learner to infer insights at the edges. Through extensive experiments, we demonstrate the strength and performance of our proposed GNN approach.

Machine learning has not achieved the same degree of success in environmental applications as in other industries. Challenges around data sparsity, quality, and consistency have limited the impact of deep neural network approaches and restricted the focus to research applications. An alternative approach – that is more amenable to the characteristics of data coming from disparate IoT devices deployed at different times and locations in the ocean – is to develop many lightweight models that can be readily scaled up or down based on the number of devices available at any time. This paper presents a serverless framework that naturally marries a single IoT sensor device with a forecasting model. Aspects related to data ingestion, data processing, model training and deployment are described. The framework is applied to a fish farm site in Atlantic Canada.