Characterising those delays proved difficult. Robust cross-correlation analysis showed only statistically detectable but weak associations between the storage-tank temperature and combustion-related operational inputs. Daily lag estimates displayed broad and heterogeneous distributions, meaning the boiler could not be described by a single deterministic response time. This thermal heterogeneity is precisely what complicates operational warning systems, since the plant’s response to combustion changes arrives at unpredictable intervals.

When the team benchmarked competing models, increasing complexity did not necessarily improve performance. A Linear autoregressive (AR) model achieved the lowest test RMSE and highest R-squared at all three horizons. Its RMSE values were 1.3774, 2.1605, and 2.6182 degrees Celsius at 60, 120, and 180 minutes respectively, with R-squared values of 0.7809, 0.4616, and 0.2104. The steady decline in accuracy with longer horizons reflects the strong persistence of the thermal system, where recent measurements carry most of the predictive information.

The study also revealed a trade-off between pointwise accuracy and coverage of delayed thermal responses. Lag coverage increased as the forecasting horizon lengthened, but predictive accuracy progressively decreased, indicating that no single horizon is universally optimal. Operators therefore face a choice between sharper short-term predictions and broader, less precise coverage of the system’s delayed behaviour.

A retrospective out-of-band warning analysis underscored this tension. XGBoost recall fell from 0.5343 at 60 minutes to 0.1761 at 120 minutes and just 0.0538 at 180 minutes, while specificity rose from 0.9095 to 0.9546 and 0.9854. In other words, longer-horizon forecasts became increasingly conservative, flagging fewer future out-of-band states but doing so with fewer false alarms.

The authors caution that multi-horizon forecasts should be interpreted as predictive risk indicators rather than evidence of causal improvements in boiler control or operational performance. For thermally delayed biomass systems, the practical message is that simple temporal models remain highly competitive, and that warning thresholds must be tuned to each horizon’s distinct accuracy and coverage profile.

Subject of Research: Multi-horizon forecasting of thermal-storage-tank temperature in a thermally delayed biomass-fired boiler system

Article Title: Multi-horizon forecasting for decision support in a thermally delayed biomass-fired boiler system

Article References: Park, S., Yang, J., Kim, S., Hwang, K., Lee, J., & Ryu, S. (2026). Multi-horizon forecasting for decision support in a thermally delayed biomass-fired boiler system. PLOS One, 21(10), e0361121. https://doi.org/10.1371/journal.pone.0361121

Image Credits: AI Generated

DOI: 10.1371/journal.pone.0361121

Keywords: biomass boiler, thermal storage, forecasting, autoregressive model, XGBoost, machine learning, time-series analysis, thermal lag, decision support, out-of-band warning, Multi-horizon, decision