End-to-End Deep Neural Network Based Nonlinear Model Predictive Control: Experimental Implementation on Diesel Engine Emission Control
Abstract
:1. Introduction
- Developed a transient Indicated Mean Effective Pressure (IMEP), Maximum Pressure Rise Rate (MPRR), and PM concentration model using a DNN with one LSTM layer, which provides a high-accuracy model for nonlinear model predictive combustion engine control;
- Real-time implementation of our previously proposed novel approach [37] to augment LSTM in NMPC (LSTM-NMPC) by augmenting LSTM hidden and cell states into a nonlinear optimization problem;
- Design and real-time implementation of an NMPC using an ML model to minimize engine-out emission concentration, optimize -PM trade off, and minimize fuel consumption, while maintaining the same output torque performance and illustrating significant improvements compared with the Cummins-calibrated production ECU.
2. Modeling
2.1. Deep Neural Network
2.2. Training Model: Diesel Engine Modeling
3. Controller Design
3.1. Nonlinear Model Predictive Control
3.2. Nonlinear State-Space Representation
3.3. Optimal Control Problem
3.4. Implementation and Deployment to Real-Time Hardware
4. Experimental Results: Diesel Emission Control
4.1. Experimental Results in Changing IMEP
4.2. Experimental Results in Changing Engine Speed
4.3. LSTM-NMPC vs. Cummins-Calibrated ECU
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Parameter | Specification | |
---|---|---|
Processor | dSPACE® 1401 | IBM PPC-750GL |
Speed | 900 MHz | |
Memory | 16 MB main memory | |
I/O | dSPACE® 1511 | |
Analog input | 16 Parallel channels | |
Resolution | 16 bit | |
Sampling frequency | 1 Msps | |
Analog output | 4 Channels | |
Digital input | 40 Channels | |
Digital output | 40 Channels | |
FPGA | dSPACE® 1514 | Xilinx® Kintex-7 |
Flip-flops | 407,600 | |
Lookup table | 203,800 | |
Memory lookup table | 64,000 | |
Block RAM | 445 | |
DSP | 840 | |
I/O | 478 |
Name | Value |
---|---|
Optimizer | Adam |
Maximum Epochs | 5000 |
Mini batch size | 512 |
Learn rate drop period | 1000 Epochs |
Learn rate drop factor | 0.5 |
L2 Regularization | 10 |
Initial learning rate | 0.001 |
Validation frequency | 64 iteration |
Momentum | 0.9 |
Squared gradient decay | 0.99 |
Unit | Training | Validation | Testing | |
---|---|---|---|---|
[bar] | 0.3 | 0.3 | 0.4 | |
[%] | 7.0 | 8.8 | 9.7 | |
[ppm] | 18.4 | 39.3 | 46.9 | |
[%] | 2.9 | 6.2 | 7.4 | |
[mg/m] | 0.4 | 1.3 | 2.4 | |
[%] | 1.2 | 4.0 | 7.5 | |
[bar/CAD] | 0.2 | 0.2 | 0.2 | |
[%] | 2.4 | 2.6 | 2.7 |
Lower Bound | Variable | Upper Bound |
---|---|---|
Case | Reference | Avg IMEP [bar] | Avg Engine | Avg | Thermal | Avg NOx | Avg PM | |
---|---|---|---|---|---|---|---|---|
Number | IMEP [bar] | BM | NMPC | Speed [rpm] | FQ [%] | Eff. [%] | [%] | [%] |
1 | 5.0 | 4.8 | 5.1 | 1190 | −7.9 | +4.7 | −18.9 | −40.8 |
2 | 5.0 | 5.2 | 4.9 | 1296 | −11.0 | +1.8 | −11.2 | −35.3 |
3 | 5.0 | 5.0 | 4.9 | 1701 | −10.4 | +3.0 | +17.0 | −14.3 |
4 | 5.0 | 5.0 | 4.8 | 1801 | −9.6 | +2.1 | +3.4 | −15.4 |
5 | 2.0 | 2.3 | 2.0 | 1509 | −14.9 | +0.1 | −22.4 | −8.0 |
6 | 3.0 | 3.1 | 3.0 | 1504 | −8.3 | +1.4 | −8.7 | −36.4 |
7 | 4.0 | 3.9 | 4.0 | 1504 | −7.9 | +3.1 | +6.7 | −37.5 |
8 | 5.0 | 4.9 | 4.9 | 1503 | −8.5 | +3.0 | +9.1 | −43.6 |
9 | 6.0 | 6.0 | 6.0 | 1504 | −7.3 | +3.2 | +20.7 | −34.2 |
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Share and Cite
Gordon, D.C.; Norouzi, A.; Winkler, A.; McNally, J.; Nuss, E.; Abel, D.; Shahbakhti, M.; Andert, J.; Koch, C.R. End-to-End Deep Neural Network Based Nonlinear Model Predictive Control: Experimental Implementation on Diesel Engine Emission Control. Energies 2022, 15, 9335. https://doi.org/10.3390/en15249335
Gordon DC, Norouzi A, Winkler A, McNally J, Nuss E, Abel D, Shahbakhti M, Andert J, Koch CR. End-to-End Deep Neural Network Based Nonlinear Model Predictive Control: Experimental Implementation on Diesel Engine Emission Control. Energies. 2022; 15(24):9335. https://doi.org/10.3390/en15249335
Chicago/Turabian StyleGordon, David C., Armin Norouzi, Alexander Winkler, Jakub McNally, Eugen Nuss, Dirk Abel, Mahdi Shahbakhti, Jakob Andert, and Charles R. Koch. 2022. "End-to-End Deep Neural Network Based Nonlinear Model Predictive Control: Experimental Implementation on Diesel Engine Emission Control" Energies 15, no. 24: 9335. https://doi.org/10.3390/en15249335