Abstract:
To reduce the number of sensors required in agricultural diesel engine Selective Catalytic Reduction (SCR) systems and provide accurate feedback for state estimation, this study proposes the use of a Multi Innovation-Singular Value Decomposition-Unscented Kalman Filter (MI-SVD-UKF) algorithm. This algorithm is specifically designed to estimate three critical state variables in the SCR system: the downstream NO
x concentration, NH
3 concentration, and ammonia coverage ratio. The study begins by developing a physical model of the SCR system using Matlab/Simulink. The model parameters are identified using a parameter estimation tool, specifically the least squares method, to simulate the dynamic behavior of the catalyst. Experimental bench data is then used to validate the identified model parameters, ensuring that the model reflects real-world operating conditions. Traditional state estimation methods, such as the Unscented Kalman Filter (UKF), present significant challenges when applied to SCR systems. These challenges include inefficient utilization of historical data, which impacts the precision of state estimation, and the occurrence of non-positive definite covariance matrices during simulations, which may lead to algorithm failure. To address these issues, the study integrates Multi Innovation (MI) theory, Singular Value Decomposition (SVD), and the UKF algorithm. This integration significantly enhances the real-time state estimation process for SCR systems by improving the accuracy and stability of the estimation, while also accelerating the convergence rate. The study enhances the state estimation accuracy by transforming single innovations into a multi-innovation matrix, leveraging MI theory. Specifically, MI theory improves data utilization by combining multiple historical data points. Additionally, Singular Value Decomposition (SVD) is applied to optimize the covariance matrix, ensuring its positive definiteness. This optimization prevents the issue of non-positive definite covariance matrices encountered in traditional UKF methods, thereby improving the algorithm’s accuracy and stability. The proposed MI-SVD-UKF algorithm is simulated and validated according to the World Harmonized Transient Cycle (WHTC) emission test standard. Thermal cycles are used to simulate real-world operating conditions and validate the performance of the state observation algorithm. Experimental results demonstrate that the MI-SVD-UKF algorithm provides more accurate estimates compared to traditional methods. Specifically, the algorithm achieves average absolute errors (MAE) of 0.807 mg/m³, 0.040 mg/m³, and 0.007 for the estimated SCR downstream NO
x concentration, NH
3 concentration, and ammonia coverage ratio, respectively. These results show substantial improvements over the traditional UKF method, with MAE reductions of 46.41%, 78.02%, and 93.33%, respectively. Furthermore, when compared to the Multi Innovation Extended Kalman Filter (MIEKF), the MI-SVD-UKF algorithm outperforms it, with MAE reductions of 80.02%, 94.03%, and 93.46%, respectively. One of the key advantages of the MI-SVD-UKF algorithm is its rapid convergence speed. When all three state variables are initialized to zero, the algorithm converges to the correct state values in just 11 seconds, demonstrating its ability to adapt quickly to changing conditions. This fast convergence ensures that the algorithm is highly suitable for real-time SCR state estimation, making it an effective solution for dynamic system environments. The findings of this study confirm that the MI-SVD-UKF algorithm can accurately estimate the SCR system's state, offering precise feedback that is essential for SCR control.