Control Oriented NOx and Soot Models for Diesel Engines

Mrosek, Matthias; Sequenz, Heiko; Isermann, Rolf

doi:10.3182/20100712-3-de-2013.00074

Cited by 15 publications

(9 citation statements)

References 7 publications

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“…. 3, as defined in (21) are illustrated in Figure 6. The model for soot emissions estimates the soot mass flow (mg/s) with an average relative error of 29% for the validation data when eight nodes are used.…”

Section: B Emission Model Resultsmentioning

confidence: 99%

“…From the measurements, 90% of the data points were randomly chosen to be used to optimize the model parameters, and the remaining 10% of the data points were used for validation. The parameters in the models for NO X (21) and soot (22) emissions were optimized according to (17). A first order difference regularisation was applied to the data fitting, where a leave-one-out cross-validation strategy was used to set the value of the regularisation coefficient λ according to the description in Section II-B.…”

Section: A Model Complexity Investigationmentioning

confidence: 99%

“…Several different types of data-driven emission models are described in the literature. Examples of this are models based on neural networks [2], [4], models based on Gaussian processes [3], global regression models [5], and global-local model approaches where a global model for the emissions is constructed by switching or weighing between different local models depending on the engine speed and injected fuel operating point of the engine [21], [16], [14]. This paper will discuss some specific data-driven model structures suitable for prediction of NO X and soot.…”

Section: Introductionmentioning

confidence: 99%

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Data-driven emission model structures for diesel engine management system development

Grahn

Johansson

McKelvey

2014

International Journal of Engine Research

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This paper discusses some specific data-driven model structures suitable for prediction of NOX and soot emissions from a diesel engine. The model structures can be described as local linear regression models where the regression parameters are defined by two-dimensional look-up tables. It is highlighted that this structure can be interpreted as a B-spline function. Using the model structure, models are derived from measured engine data. The smoothness of the derived models is controlled by using an additional regularization term and the globally optimal model parameters can be found by solving a linear least-squares problem. Experimental data from a 5-cylinder Volvo passenger car diesel engine is used to derive NOX and soot models, using a leave-one-out cross validation strategy to determine the optimal degree of regularization. The model for NOX emissions predicts the NOX mass flow with an average relative error of 5.1% and the model for soot emissions predicts the soot mass flow with an average relative error of 29% for the measurement data used in this study. The behavior of the models for different engine management system settings regarding boost pressure, amount of exhaust gas recirculation, and injection timing has been studied. The models react to the different engine management system settings in an expected way, making them suitable for optimization of engine management system settings. Finally, the model performance dependence on the selected model complexity, and on the number of measurement data points used to derive the models has been studied.

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Section: B Emission Model Resultsmentioning

confidence: 99%

Section: A Model Complexity Investigationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Data-driven emission model structures for diesel engine management system development

Grahn

Johansson

McKelvey

2014

International Journal of Engine Research

View full text Add to dashboard Cite

show abstract

“…A mean value emission model which simplifies the combustion as a batch process is presented in Mrosek et al (2010). The dynamics in the emission formation arise from the cylinder charge composition at intake valve closing and the injection parameters.…”

Section: Introductionmentioning

confidence: 99%

“…The exhaust gas measurement sensors have further sensor dynamics. Usually a first order lag and dead time model is applied to model the sensor dynamics (Schilling, 2008;Mrosek et al, 2010). As the dynamics after the emission formation vary with the engine operation point and these models can only approximate the measurement dynamics, a more detailed modelling of the measurement dynamics is necessary.…”

Section: Introductionmentioning

confidence: 99%