Towards an approach to multivariate outlier detection for District Heating System data
Authors: Rajko Turudija, Dušan Stojiljković, Milan Zdravković, Marko Ignjatović
Abstract
In this paper, we test different methods for multivariate detection of outliers in the data of transmitted heat energy in the selected substation of local District Heating System, by also considering outside ambient temperature, namely Z-score (univariate, as a benchmark), Mahalanobis distances, Principal Component Analysis (PCA), Isolation Forest and Hotelling's T-squared test. The overall research aims at uncovering irregular plant operation, with a wider objective of identifying the opportunities for reducing the consumption of gas in central heating plants as well as the CO2 emission. The proposed approach considers specific domain circumstances, such as irrelevance of zero transmit-ted energy timepoints as indication of off-grid plant. The outcomes of the different methods are discussed with domain experts. It was concluded that PCA, Isolation Forest and Hotelling method provide relevant results. Finally, we adopt the ensemble method (selection based on the agreement of all three methods on the detected outliers) as the final approach.
Matrix-variate distributions are a relatively recent addition to the model-based clustering literature, thereby making it possible to analyze data in matrix form with complex structure such as images and time series. Due to its recent appearance, there is limited literature on matrix-variate data, with even less on dealing with outliers in these models. An approach for clustering matrix-variate normal data with outliers is discussed. The approach, which uses the distribution of subset log-likelihoods, extends the OCLUST algorithm to matrix-variate normal data and uses an iterative approach to detect and trim outliers.
This paper presents a comparative study of two distinct approaches, XGBoost and Long-Short Term Memory (LSTM), for forecasting transmitted heat energy in District Heating Systems (DHS). The objective is to explore scenarios in which conventional ML algorithms demonstrate better performance over deep learning networks in time series forecasting and the associated benefits in terms of computational cost and environmental impact. The study focuses on a real-world DHS dataset. Through experimentation and analysis, it is demonstrated that XGBoost consistently outperforms LSTM in this specific forecasting task. The difference is explained by the error distribution illustrating that LSTM makes more significant errors in the intervals of less data availability. The reduced computational demands of conventional ML approaches not only result in cost savings but also minimize the carbon footprint associated with data analysis tasks in energy systems.
Out-of-distribution (OOD) detection is essential for reliable deployment of deep learning systems, yet the majority of existing methods are evaluated on small, visually homogeneous benchmarks. In this work, we study six OOD detection methods spanning post-hoc scoring, auxiliary objectives, energy-based models, and constrained optimization on the Plant Pathology 2021 dataset, a fine-grained task with natural distribution shifts. Energy-based fine-tuning performs best across OOD settings, improving detection over the softmax baseline while preserving in-distribution accuracy. Analysis shows these gains stem from both a restructuring of the embedding space alongside calibration of the scoring function. We further document practical training instabilities that arise when scaling constrained optimization methods to moderate-sized datasets, findings that are largely absent from existing literature. Our results demonstrate that principled OOD detection is achievable on real-world domain-specific data and that benchmark evaluations alone may not capture the challenges that emerge in practice.