Advantages and Applications of Transforming Empirical Model Input Space with Dimensional Models

Model-based calibration of steady-state engine operation is commonly performed with highly parameterized empirical models that are accurate but not very robust, particularly when predicting highly nonlinear responses such as diesel smoke emissions. To address this problem, and to boost the accuracy of more robust non-parametric methods to the same level, GT-Power was used to transform the empirical model input space into multiple input spaces that simplified the input-output relationship and improved the accuracy and robustness of smoke predictions made by three commonly used empirical modeling methods: Multivariate Regression, Neural Networks and the k-Nearest Neighbor method. The availability of multiple input spaces allowed the development of two committee techniques: a 'Simple Committee' technique that used averaged predictions from a set of 10 pre-selected input spaces chosen by the training data and the "Minimum Variance Committee" technique where the input spaces for each prediction were chosen on the basis of disagreement between the three modeling methods. This latter technique equalized the performance of the three modeling methods. The successively increasing improvements resulting from the use of a single best transformed input space (Best Combination Technique), Simple Committee Technique and Minimum Variance Committee Technique were verified with hypothesis testing. The transformed input spaces were also shown to improve outlier detection and to improve k-Nearest Neighbor performance when predicting dynamic emissions with steady-state training data. An unexpected finding was that the benefits of input space transformation were unaffected by changes in the hardware or the calibration of the underlying GT-Power model.

Reduction of Transient Particulate Matter Spikes with Decision Tree Based Control

Decision trees have been proposed as a basis for modifying table based injection to reduce transient particulate spikes during the turbocharger lag period. It has been shown that decision trees can detect particulate spikes in real time. In well calibrated electronically controlled diesel engines these spikes are narrow and are encompassed by a wider NOx spike. Decision trees have been shown to pinpoint the exact location of measured opacity spikes in real time thus enabling targeted PM reduction with near zero NOx penalty. A calibrated dimensional model has been used to demonstrate the possible reduction of particulate matter with targeted injection pressure pulses. Post injection strategy optimized for near stoichiometric combustion has been shown to provide additional benefits. Empirical models have been used to calculate emission tradeoffs over the entire FTP cycle. An empirical model based transient calibration has been used to demonstrate that such targeted transient modifiers are more beneficial at lower engine-out NOx levels.

Analysis and Prediction of Transient Opacity Spikes Using Dimensional Modeling

Dimensional modeling, GT-Power in particular, has been used for two related purposes-to quantify and understand the inaccuracies of transient engine flow estimates that cause transient smoke spikes and to improve empirical models of opacity or particulate matter used for engine calibration. It has been proposed by dimensional modeling that exhaust gas recirculation flow rate was significantly underestimated and volumetric efficiency was overestimated by the electronic control module during the turbocharger lag period of an electronically controlled heavy duty diesel engine. Factoring in cylinder-to-cylinder variation, it has been shown that the electronic control module estimated fuel-Oxygen ratio was lower than actual by up to 35% during the turbocharger lag period but within 2% of actual elsewhere, thus hindering fuel-Oxygen ratio limit-based smoke control. The dimensional modeling of transient flow was enabled with a new method of simulating transient data in which the manifold pressures and exhaust gas recirculation system flow resistance, characterized as a function of exhaust gas recirculation valve position at each measured transient data point, were replicated by quasi-static or transient simulation to predict engine flows. Dimensional modeling was also used to transform the engine operating parameter model input space to a more fundamental lower dimensional space so that a nearest neighbor approach could be used to predict smoke emissions. This new approach, intended for engine calibration and control modeling, was termed the "nonparametric reduced dimensionality" approach. It was used to predict federal test procedure cumulative particulate matter within 7% of measured value, based solely on steady-state training data. Very little correlation between the model inputs in the transformed space was observed as compared to the engine operating parameter space. This more uniform, smaller, shrunken model input space might explain how the nonparametric reduced dimensionality approach model could successfully predict federal test procedure emissions when roughly 40% of all transient points were classified as outliers as per the steady-state training data.