State estimation of SCR for agricultural diesel engine based on MI-SVD-UKF algorithm

A selective catalytic reduction (SCR) system aims to minimize the emissions of particulate matter and nitrogen oxides (NO_x) in agricultural diesel engines. However, the traditional estimation of the SCR state, such as the unscented Kalman filter (UKF), has presented the inefficient utilization of historical data and the non-positive definite covariance matrices during simulations, leading to low precision and algorithm failure. In this study, a multi innovation-singular value decomposition-unscented Kalman filter (MI-SVD-UKF) algorithm was proposed to reduce the number of sensors for the accurate feedback of the SCR state estimation. Multi innovation (MI), singular value decomposition (SVD), and the UKF algorithm were integrated to significantly enhance the real-time estimation of the SCR state. The accuracy and stability of the estimation were also improved to accelerate the convergence rate. The accuracy of the state estimation was enhanced to transform the single innovations into a multi-innovation matrix using MI theory. Specifically, the MI theory improved the data utilization to combine the multiple historical data points. Additionally, the SVD was applied to optimize the covariance matrix for positive definiteness. This optimization prevented the non-positive definite covariance matrices in the traditional UKF, thereby improving the algorithm’s accuracy and stability. Specifically, three variables of SCR state were designed as the downstream NO_x concentration, NH₃ concentration, and ammonia coverage ratio. A physical model of the SCR system was developed using Matlab/Simulink software. The parameters of the model were identified to estimate using the least squares method. The dynamic behavior of the catalyst was simulated after identification. A bench test was then carried out to validate the parameters in real-world conditions. The MI-SVD-UKF algorithm was simulated and validated according to the world harmonized transient cycle (WHTC) emission test standard. Thermal cycles were used to simulate the real-world conditions and then validate the performance of the state observation. Experimental results demonstrate that the MI-SVD-UKF algorithm achieved more accurate estimates, compared with the traditional one. Among them, the average absolute errors (MAE) of 0.807 mg/m³, 0.040 mg/m³, and 0.007 were obtained for the estimated SCR downstream NO_x concentration, NH3 concentration, and ammonia coverage ratio, respectively. There were substantial improvements over the traditional UKF, with the MAE reductions of 0.699 mg/m³, 0.142 mg/m³, and 0.098, respectively. Furthermore, the MI-SVD-UKF algorithm outperformed with the MAE reductions of 3.232 mg/m³, 0.630 mg/m³, and 0.100, respectively, compared with the multi innovation extended Kalman filter (MIEKF). The high convergence speed was also achieved in the MI-SVD-UKF algorithm. Once all three state variables were initialized to zero, the algorithm converged to the correct state values in just 11 s, in order to rapidly adapt to the varying conditions. This high convergence was highly suitable for the real-time estimation of the SCR state, indicating an effective solution to the dynamic environments. As such, the MI-SVD-UKF algorithm can be expected to accurately estimate the state of the SCR system. The findings can also offer precise feedback to the SCR control.