Prediction interval soft sensor for dissolved oxygen content estimation in an electric arc furnace

In this study, a novel soft sensor modeling approach using Takagi–Sugeno (TS) fuzzy models and Prediction Intervals (PIs) is presented to quantify uncertainties in Electric Arc Furnace (EAF) steel production processes, namely to estimate the dissolved oxygen content in the steel bath. In real EAF operation, dissolved oxygen content is measured only a few times in the refining stage; therefore, the approach addresses the challenge of predicting unobserved output under conditions of irregular and scarce output measurements, using two distinct methods: Instant TS (I-TS) and Input Integration TS (II-TS). In the I-TS method, the model is computed for each individual indirect measurement, while the II-TS approach integrates these indirect measurements. The inclusion of PIs in TS models allows the derivation of the narrowest band containing a prescribed percentage of data, despite the presence of heteroscedastic noise. These PIs provide valuable insight into potential variability and allow decision-makers to evaluate worst-case scenarios. When evaluated against real EAF data, these methods were shown to effectively overcome the obstacles posed by scarce output measurements. Despite its simplicity, the I-TS model performed better in terms of interpretability and robustness to the operational reality of the EAF process. The II-TS model, on the other hand, showed excellent performance on all metrics but exhibited theoretical inconsistencies when deviating from typical operations. In addition, the proposed method successfully estimates carbon content in the steel bath using the established dissolved oxygen/carbon equilibrium, eliminating the need for direct carbon measurements. This shows the potential of the proposed methods to increase productivity and efficiency in the EAF steel industry.