B-splines for Diesel Engine Emission Modeling

• The equivalence between linear interpolation and B-spline functions of degree 1 is described. The equivalence is used to express interpolation based diesel engine NOX and soot emission models as B-spline functions, and to apply data fitting methods for B-spline functions to perform calibration of the models. This strategy leads to that the model calibration can be calculated directly by means of analytically solving a minimization problem. The B-spline representation also makes it possible to control the smoothness and extrapolation behavior of the interpolation maps in the models in a controlled manner. The models have been calibrated using measured steady-state data from a 5-cylinder Volvo passenger car diesel engine with a displacement volume of 2.4 liters, equipped with a turbocharger, an exhaust gas recirculation system, and a common rail injection system. The calibrated model for NOX emissions predicts the NOX mass ow with a root mean square error of 1.6 mg/s, and the calibrated model for soot emissions predicts the soot mass ow with a root mean square error of 0.65 mg/s. The described equivalence between linear interpolation and B-spline functions of degree 1 could also be used for calibration of other models of similar structure.

Subject headings

TEKNIK OCH TEKNOLOGIER  -- Maskinteknik -- Annan maskinteknik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Mechanical Engineering -- Other Mechanical Engineering (hsv//eng)

TEKNIK OCH TEKNOLOGIER  -- Elektroteknik och elektronik -- Reglerteknik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Electrical Engineering, Electronic Engineering, Information Engineering -- Control Engineering (hsv//eng)

TEKNIK OCH TEKNOLOGIER  -- Elektroteknik och elektronik -- Signalbehandling (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Electrical Engineering, Electronic Engineering, Information Engineering -- Signal Processing (hsv//eng)

Keyword

Interpolation

Splines

Diesel engines

Engine modeling

Publication and Content Type

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