Virtual sensors for transient diesel soot and NOx emissions: Neuro-fuzzy model tree with automatic relevance determination

The paper describes development of virtual sensors for transient diesel particulate and NO_X emissions. The emission models developed in this paper belong to the family of hierarchical models, namely “neuro-fuzzy model tree”. The modeling techniques are motivated by the idea of divide and conquer the input-output space. The complex problem is divided into multiple simpler subproblems, which are then identified using simpler class of models. A specially designed multi-pseudo random perturbation signal and experimental tests are proposed to generate training data. The diesel engine is tested using integrated hardware and software tools for automated testing with high speed data recording. The engine out transient NO_X and soot emission is recorded using fast emission analyzers. The data is then used to construct neuro-fuzzy model with Gaussian validity functions and local neural networks. An automatic relevance determination (ARD) derived from Baye´s framework is derived and applied for choosing appropriate model inputs and reducing the model complexity. Finally, the model is validated with testing data recorded during Engine-in-the-Loop (EIL) testing of engine coupled to virtual hybrid powertrain. It is shown that the prediction accuracy of the proposed models, both qualitatively and quantitatively, are very good with low computational cost.