A multivariate approach for fuzzy prediction interval design and its application for a climatization system forecasting

• Published in: Expert systems with applications Vol. 255; p. 124715
• Main Authors: Cartagena, Oscar, Trovò, Francesco, Sáez, Doris
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01-12-2024
• Subjects: Climatization systems; Coupled dynamical systems; Fuzzy systems; Interval modeling; Multivariate modeling; Prediction interval; Coupled dynamical systems; Interval modeling; Climatization systems; Multivariate modeling; Prediction interval; Fuzzy systems
• ISSN: 0957-4174
• DOI: 10.1016/j.eswa.2024.124715

The existing uncertainties present during the operation of dynamic processes could affect the performance of modeling systems, control strategies, and fault detection systems. Because of that, the study of uncertainty quantification and the design of prediction intervals has recently gained interest in representing the effect of uncertainty on future process behavior. However, these tools have been designed to focus on applying multiple-input single-output (MISO) systems. For this reason, this work aims to design a novel multiple-variable uncertainty region that results from the adaptation of prediction interval methods to a multiple-input multiple-output (MIMO) framework. To achieve this goal, the algorithm integrates the information provided by the prediction intervals identified for each separate output variable and the covariance matrix of the past error vectors to determine the ellipsoid region that will contain the future values of the modeled MIMO system. How this proposal handles the uncertainty effect of these multiple output variables is tested over simulated data from a coupled Hénon map and real data from a heating, ventilation, and air conditioning system. The simulation results achieved in this work show the proposal’s effectiveness in characterizing the uncertainty of multiple variables simultaneously when compared to applying the direct combination of multiple MISO prediction intervals.
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•This work extends the concept of prediction intervals for multiple output systems.•Multivariate uncertainty modeling is proposed based on principal component analysis.•The Resulting multivariate uncertainty region is tested by modeling a coupled Hénon map.•The proposal is used to characterize the uncertainty in a climatization system.