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Application of stochastic design optimization to a passenger car diesel engine to reduce emission spread in a vehicle fleet

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Abstract

This paper demonstrates the advantages of stochastic design optimization on a passenger car diesel engine: the emission distribution in the vehicle fleet can be significantly reduced by optimizing the base engine calibration taking into account component tolerances. This paper is an extension to the work presented in [25]. The conventional calibration approach of using empirical safety coefficients is replaced by explicitly taking into account the uncertainty stemming from manufacturing tolerances. The method enables us to treat low-emission spread in a fleet as an optimization target. This process enables a more robust design and helps to avoid recalibration steps that potentially generate high costs. The method consists of four steps: an initial uncertainty analysis, which accounts for engine component tolerances and determines the underlying parameter uncertainty of the engine model—with parameter uncertainty being deviations in the model parameters resulting from component tolerances. Followed by a measurement campaign according to the design of experiments principles, the training of a stochastic engine model and the solving a stochastic optimization problem. The latter two are discussed in more detail. First, the stochastic models are validated on transient testbed measurements with different setups, which are subject to uncertainty. The model error for both engine-out particulate matter and nitrogen oxides (\({\text{NO}}_{{ x}}\)) is extremely low. Then, stochastic optimization is performed on a calibration task aiming to minimize engine-out PM for the entire fleet while ensuring that the \({\text{NO}}_{{ x}}\) emission remains below a given upper threshold, again for the entire fleet. Boundary constraints and smoothness constraints are employed to ensure feasibility and smooth engine maps. The optimization results are compared to the original calibration of the test engine—both for a representative nominal engine and the expected fleet behavior. The results show a significant improvement in engine-out PM while complying with the imposed constraints, including the \({\text{NO}}_{{ x}}\) emission limit for the entire fleet.

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Abbreviations

ASC:

Ammonia slip catalyst

BC:

Best case

CAC:

Charge air cooler

CAD:

Crank angle degree

CRP:

Common rail pressure

\({\text {CO}}_{{2}}\) :

Carbon dioxide

DoE:

Design of experiments

DPF:

Diesel particulate filter

ECU:

Engine control unit

EGR:

Exhaust gas recirculation

GP:

Gaussian process

LNT:

Lean \({\text{NO}}_{{ x}}\) trap

LOOCV:

Leave-one-out cross-validation

MAF:

Mass air flow sensor

MC:

Monte Carlo

MV:

Mean value

\({\text {NO}}_{{x}}\) :

Nitrogen oxides

ODCM:

Online DoE with constraint modeling

OP:

Operating point

PM:

Particulate matter

\({\text{R}}^{2}\) :

Coefficient of determination

RDE:

Real driving emissions

SCR:

Selective catalytic reduction

SE:

Squared exponential

TDCf:

Top dead center firing

VaR:

Value at Risk

WLTC:

Worldwide harmonized Light-duty vehicles Test Cycle

WC:

Worst case

\(\alpha\) :

Confidence level

\(\delta _\text{cum}\) :

Cumulative percent error

\(\phi _\text {MI}\) :

Start of injection of the main injection

\(\psi _\text {EGR,LP}\) :

Mass fraction of the low-pressure EGR

\(\mathcal {N}\) :

Normal distribution

\({m}_{{\text {CC}}}\) :

Cylinder charge

\({m}_{{\text {IAM}}}\) :

Intake air mass

\({m}_\text {Inj}\) :

Total injected fuel mass

\({m}_\text {PoI}\) :

Injected fuel mass of the post-injection

\({m}_\text {PI1}\) :

Injected fuel mass of the 1st pilot injection

\({m}_\text {PI2}\) :

Injected fuel mass of the 2nd pilot injection

\({n}_\text {Eng}\) :

Engine speed

P :

Effective power output

\({p}_\text {2}\) :

Charge pressure

\({t}_\text {PoI}\) :

Time distance between the main and the post-injection

\({t}_\text {PI1}\) :

Time distance between the second pilot and the main injection

\({t}_\text {PI2}\) :

Time distance between the first pilot and the second pilot injection

\({X}_{{\text {EGR}}}\) :

Exhaust gas recirculation rate

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Acknowledgements

The authors would like to thank Jürgen Frick, Alexandra Fritsch, and Andre Wiedersberg, for their support while conducting the engine test bench measurements used for this work. The authors would also like to thank Robert Bosch GmbH for the resources provided to produce this work.

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Authors and Affiliations

  1. Institut für Kolbenmaschinen (IFKM), Karlsruhe Institute of Technology, Karlsruhe, Germany

    Kadir Mourat & Thomas Koch

  2. Robert Bosch GmbH, Powertrain Solutions, Stuttgart-Feuerbach, Germany

    Carola Eckstein

  3. Oberrahserstraße 53, 41748, Viersen, Germany

    Kadir Mourat

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  1. Kadir Mourat
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Correspondence to Kadir Mourat.

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Mourat, K., Eckstein, C. & Koch, T. Application of stochastic design optimization to a passenger car diesel engine to reduce emission spread in a vehicle fleet. Automot. Engine Technol. 6, 99–112 (2021). https://doi.org/10.1007/s41104-021-00077-2

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