[Objective] Municipal solid waste (MSW) incineration exhibits pronounced time-varying thermal characteristics because of fluctuations in feed composition, moisture content, and operating conditions. Pure data-driven models may also suffer from error accumulation and tracking drift during continuous free-running prediction. This study aims to develop a grey-box furnace-temperature object model that combines physical interpretability with stable dynamic tracking performance under field operating conditions. 

[Methods] The grate bed was spatially discretized into a series of MSW elements, and the evolution of moisture, volatile matter, fixed carbon, and ash was described using mass-conservation and component-consumption relationships. A furnace-temperature mechanism model driven by operating commands, including primary-air distribution and grate velocity, was then established based on mass and energy conservation. To overcome the limitations of assuming a constant feed composition, an equivalent dynamic lower heating value (LHV) mechanism was introduced through element-state recursion and instantaneous spatial integration. The proposed equivalent dynamic LHV is not intended to directly estimate the actual LHV of the incoming waste; instead, it serves as an equivalent heat-source term that reflects changes in the overall composition state of the grate bed. Field DCS data were preprocessed using median absolute deviation (MAD)-based outlier detection and moving-average smoothing. A serial hybrid optimization procedure combining the Sparrow Search Algorithm and the Nelder–Mead simplex method (SSA-NM) was subsequently employed to identify eight lumped model parameters offline. SSA was used to search for a favorable parameter region over a wide solution space, whereas NM performed derivative-free local refinement using the SSA result as its initial point. 

[Results] The model was evaluated using 10 h of independent continuous DCS operating data collected after the parameter-identification period from a waste-to-energy plant. The validation interval included continuous variations in furnace temperature, air flow, flue-gas oxygen content, waste feeding rate, steam flow, and flue-gas flow, rather than a manually selected steady-state segment. The proposed model achieved a root mean square error (RMSE) of 11.91 °C and a mean absolute percentage error (MAPE) of 0.85%. Compared with the static-LHV model using empirical initial parameters, the RMSE was reduced by 54.15%. Compared with the static-LHV model after parameter identification, the RMSE was reduced by 41.13%. A conventional long short-term memory network was also established as a pure data-driven baseline under a closed-loop free-running prediction mode. The grey-box model exhibited lower prediction error and more stable trend tracking over the continuous validation interval. 

[Conclusion] The integration of an equivalent dynamic LHV mechanism with field-data-based parameter identification enables the proposed grey-box model to retain mass- and energy-conservation relationships while improving furnace-temperature tracking under time-varying operating conditions. The resulting model can provide an interpretable object-model basis for subsequent control-strategy development and operating-parameter optimization in MSW incineration systems.