A data-driven multi-objective dynamic prediction model for coal-fired boilers under deep peak shaving

Accurate simultaneous prediction of NOx emissions and superheated steam temperature is essential for environmental compliance, process safety, and efficient operation of coal-fired utility boilers. This challenge becomes more pronounced under deep peak-shaving conditions, where wide load fluctuations deteriorate denitrification efficiency of the SCR and destabilize steam temperature regulation. To address this issue, a nonlinear soft-sensor modeling framework, termed Multi-order Kolmogorov–Arnold Network enhanced iTransformer (MKAN-iTransformer), is proposed for coordinated multi-output prediction of key combustion and thermal performance indicators. The KPCA is employed to extract compact, informative representations from high-dimensional and strongly coupled process variables, mitigating redundancy and nonlinear correlations. On this basis, a MKAN is innovatively integrated into the iTransformer architecture to enhance spatiotemporal feature learning. The MKAN module adopts a dual-branch design combining Chebyshev polynomial expansions and depthwise separable convolutions, enabling the model to capture both global nonlinear trends and local multi-frequency temporal dependencies in industrial time-series data. Validation using real operational data from coal-fired utility boilers demonstrates that the proposed model achieves state-of-the-art performance compared with benchmark methods, including TCN-RNN and CNN-LSTM-Attention. Under identical conditions, the proposed MKAN-iTransformer improves the coefficient of determination (R2) by 3.72% for NOx emission prediction and 3.31% for steam temperature prediction relative to the baseline Transformer. These results indicate strong robustness and generalization capability under variable-load operating regimes. The proposed method provides an effective soft-sensing and decision-support tool for multi-objective monitoring and optimization in complex combustion systems, contributing to improved environmental performance and operational stability in industrial boiler systems.