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

Thermally delayed biomass-boiler systems exhibit heterogeneous temporal responses that complicate forecasting and operational warning. This study analysed long-term field data from a biomass-fired boiler system to characterise thermal-response lags and evaluate multi-horizon forecasting of the P1 thermal-storage-tank temperature at 60-, 120-, and 180-min horizons. Robust cross-correlation analysis showed statistically detectable but weak associations between P1 temperature and the combustion-related operational inputs, while daily lag estimates exhibited broad and heterogeneous distributions, indicating that the system could not be represented by a single deterministic response time. Benchmark comparison showed that increasing model complexity did not necessarily improve forecasting performance. The Linear AR model achieved the lowest test RMSE and highest R ² at all three horizons, with RMSE values of 1.3774, 2.1605, and 2.6182 °C and R ² values of 0.7809, 0.4616, and 0.2104 at 60, 120, and 180 min, respectively. Lag coverage increased with forecasting horizon, whereas predictive accuracy progressively decreased, demonstrating a trade-off between pointwise accuracy and coverage of delayed thermal responses rather than a universally optimal horizon. Retrospective out-of-band warning analysis further showed that XGBoost recall decreased from 0.5343 at 60 min to 0.1761 at 120 min and 0.0538 at 180 min, while specificity increased from 0.9095 to 0.9546 and 0.9854, respectively. These results indicate that longer-horizon forecasts became increasingly conservative and detected progressively fewer future out-of-band states. Overall, the findings demonstrate that simple temporal models remain highly competitive for this strongly persistent thermal system and that multi-horizon forecasts should be interpreted as predictive risk indicators rather than evidence of causal improvements in boiler control or operational performance.