A correlation-based model order reduction approach for a diesel engine NOx and brake mean effective pressure dynamic model using machine learning

A correlation-based model order reduction algorithm is developed using support vector machine to model NOx emission and break mean effective pressure of a medium-duty diesel engine. The support vector machine-based model order reduction algorithm is used to reduce the number of features of a 34-feature full-order model by evaluating the regression performance of the support vector machine-based model. Then, the support vector machine-based model order reduction algorithm is used to reduce the number of features of the full-order model. Two models for NOx emission and break mean effective pressure are developed via model order reduction, one complex model with high accuracy, called high-order model, and the other with an acceptable accuracy and a simple structure, called low-order model. The high-order model has 29 features for NOx and 20 features for break mean effective pressure, while the low-order model has nine features for NOx and six features for break mean effective pressure. Then, the steady-state low-order model and high-order model are implemented in a nonlinear control-oriented model. To verify the accuracy of nonlinear control-oriented model, a fast response electrochemical NOx sensor is used to experimentally study the engine transient NOx emissions. The high-order model and low-order model support vector machine models of NOx and break mean effective pressure are compared to a conventional artificial neural network with one hidden layer. The results illustrate that the developed support vector machine model has shorter training times (5-14 times faster) and higher accuracy especially for test data compared to the artificial neural network model. A control-oriented model is then developed to predict the dynamic behavior of the system. Finally, the performance of the low-order model and high-order model is evaluated for different rising and falling input transients at four different engine speeds. The transient test results validate the high accuracy of the high-order model and the acceptable accuracy of low-order model for both NOx and break mean effective pressure. The high-order model is proposed as an accurate virtual plant while the low-order model is suitable for model-based controller design.