An indicated torque estimation method based on the Elman neural network for a turbocharged diesel engine

A model-based indicated torque estimation method for a turbocharged diesel engine is presented in this study. The proposed model consists of two submodels: a steady-state indicated torque model; a transient torque coefficient model using the Elman neural network. Experiments are designed to acquire the database for the model. The optimal parameters of the Elman neural network are determined; the results show that the mean absolute percentage error of the transient torque coefficient for the estimated values using the Elman neural network and the experimental values is within 2% and the maximum error is about 7%. A comparison of the usability of the back-propagation network and that of the Elman neural network for transient estimation problems is studied; the results show that the Elman neural network is more applicable in terms of the transient accuracy and the convergence time. To validate the accuracy of the model, the experimental results for a new engine speed with two new processes are employed as test data; it is shown that the mean absolute percentage error of the indicated torque is within 2% and the maximum error is about 6%. Furthermore, explicit formulation of the Elman neural network model is acquired and rewritten as C code. Then, online validation is conducted and the results show that the mean absolute percentage error of the indicated torque is within 6%, with a maximum error of 15%.