Modeling Virtual Sensor for Engine Nitrogen Oxides Using Variants of Artificial Neural Networks

Virtual sensing or estimation of emission species such as NOx at the engine exhaust using the appropriate engine measurables and leveraging it for control/diagnosis is a challenging task given the highly nonlinear and dynamic nature of the combustion process. This article presents development of virtual engine-out NOx (EONOx) sensor using two different supervised dynamic artificial neural network (ANN) topologies, namely, trained recurrent neural network (RNN) and wavelet neural network (WNN). The proposed RNN architecture is a single hidden layer neural network with permutations of feedback connections between the inter- and intra-layer nodes. The RNN resembles a nonlinear state-space model mapping select engine measurables and the engine-out NOx and is trained using a variant of real-time recurrent learning (RTRL) algorithm. The WNN architecture is a single hidden layer neural network comprising hidden layer nodes with wavelets as activation functions. The activation functions of the WNN nodes are adapted for their form and time shift along with their synaptic weights in the supervised learning method. The topologies are validated in virtual environment using modeled data as well as experimental data. Approaches toward leveraging these virtual sensors for better NOx control, both at the engine-out and system-out level are discussed along with their benefits. The limitations of such data-based virtual sensors are stated. The outcome of this work is methodology to select appropriate ANN topology and training it for efficient EONOx virtual sensor and leveraging it for control at engine and tailpipe level.