Virtual sensors for transient diesel soot and NO<inf>x</inf> emissions: Neuro-fuzzy model tree with automatic relevance determination

Abstract

Abstract² 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 KLHUDUFKLFDO PRGHOV QDPHO\ ³QHXUR-IX]]\ PRGHO WUHH´ 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 neurofuzzy model with Gaussian validity functions and local neural networks. An automatic relevance determination (ARD) GHULYHG IURP %D\H ¶V IUDPHZRUN LV GHULYHG DQG DSSOLHG IRU 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.Index Terms² transient diesel emissions, neuro-fuzzy model, hierarchical models, automatic relevance determination (ARD), neural networks, multi-level pseudo random signal (MPRS)

Neuro-fuzzy model tree approach to virtual sensing of transient diesel soot and NOx emissions

“…In the next subsections, we briefly describe the LNFMT and generation of training data for developing models. More details can be found in the earlier work by Johri et al 23,24…”

“…26 This information is used to create m-PRS signal with appropriate frequency range, switching time and amplitude level. 23,24…”

“…Next, the emission models are developed using the neuro-fuzzy training algorithm. 23,24 The algorithm has two loops. The outer loop optimizes the input space partitioning while the inner loop calculates the relevant input signals and optimal weights for each particular local model.…”

“…The first level models are further partitioned into multiple local models (leaf nodes) using the neuro-fuzzy algorithm. 23,24 The overall model output is calculated by summing the contributions of every local model at leaf nodes weighted with their validity function values. The validity functions pass their contribution to the next higher node (parent)…”

Causal, Correlation and Automatic Relevance Determination Machines for Granger Causality

“…The ARD has been applied successfully in many areas including trading (Shutin and Buchgraber, 2012), in missing data estimation (Duma et al, 2012), in virtual sensors in diesel soot (Johri et al, 2012), in image classification (Zhang et al, 2012), in (Huang et al, 2012) and to model antenna input characteristics (Jacobs, 2012).…”