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基于MI-SVD-UKF算法的农用柴油机SCR状态估计

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

  • 摘要: 为减少农用柴油机SCR(selective catalytic reduction)催化器传感器数量,精确提供SCR状态反馈,该研究提出使用多新息奇异值分解-无迹卡尔曼滤波(multi innovation-singular value decomposition-unscented kalman filter, MI-SVD-UKF)算法对SCR系统下游NOx浓度、NH3浓度和氨覆盖率3个状态量进行估计。首先基于Matlab/Simulink对SCR系统进行物理建模,并利用最小二乘法对模型参数进行辨识,以模拟催化器的动态变化。针对无迹卡尔曼滤波在估计SCR状态时存在对历史数据利用率低,仿真中出现协方差矩阵非正定情况使算法失效的问题,利用多新息MI(multi innovation)理论、奇异值SVD(singular value decomposition)分解和无迹卡尔曼滤波UKF(unscented kalman filter)算法相结合对SCR状态进行在线估计。根据世界统一瞬态循环(world harmonized transient cycle, WHTC)排放测试标准,利用热循环对模型观测算法进行仿真和验证。试验验证结果表明:基于MI-SVD-UKF算法对SCR下游NOx浓度、NH3浓度和氨覆盖率估计值的平均绝对误差(MAE)分别为0.807 mg/m3、0.040 mg/m3和0.007,能对SCR系统状态进行精确估计,与传统UKF相比,其MAE分别降低了46.41%、78.02%和93.33%,与多新息扩展卡尔曼滤波(multi innovation extended kalman filter, MIEKF)相比,其MAE分别降低了80.02%、94.03%和93.46%;在3个估计状态量初始值均设置为0时,经过11 s可收敛到状态初始值,收敛速度较快,证明了所提算法能准确估计SCR系统状态,可为实现SCR控制提供状态反馈。

     

    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 NOx concentration, NH3 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 NOx concentration, NH3 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.

     

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