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

Abstract

A correlation-based model order reduction algorithm is developed using support vector machine to model [Formula: see text] 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 [Formula: see text] 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 [Formula: see text] and 20 features for break mean effective pressure, while the low-order model has nine features for [Formula: see text] 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 [Formula: see text] sensor is used to experimentally study the engine transient [Formula: see text] emissions. The high-order model and low-order model support vector machine models of [Formula: see text] 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 [Formula: see text] 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.