# Applying Density-Based Clustering for the Analysis of Emission Events in Real Driving Emissions Calibration

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

#### State-of-the-Art—Novel Methods for Vehicle Calibration

## 2. Materials and Methods

- Event-based RDE validation using multiple test environments.
- Identification of calibration potentials.
- Quantification of statistical safety.
- Dynamic and predictive cycle generation.

#### 2.1. Data Source

_{X}emission intensities using event detection, as described in Section 2.2, and transformed into $959$ events. The measurements carried out include temperatures between $-7\xb0\mathrm{C}$ and $35\xb0\mathrm{C}$. In addition to WLTC measurements, $7$ different RDE speed profiles were tested on an emission chassis dynamometer test bench. Furthermore, $2$ different routes in different drive modes were tested with a portable emission measurement system (PEMS) on-road. The tests were carried out with stabilized exhaust aftertreatment systems ($>3000\mathrm{k}\mathrm{m}$, $~70\%$ of the driven tests) as well as aged exhaust aftertreatment systems ($~30\%$ of the driven tests). All data were resampled to a $1\mathrm{H}\mathrm{z}$ frequency prior to the event detection as most of the emission measurements are only available in this resolution.

#### 2.2. Events and Event Detection

#### 2.3. Pre-Processing of Events and Distance Calculation

#### 2.4. Clustering Method

- Minimum cluster size ${C}_{\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{S}\mathrm{i}\mathrm{z}\mathrm{e}}$.
- Minimum density ${\rho}_{\mathrm{m}\mathrm{i}\mathrm{n}}$.
- Minimum distance between two clusters ${\epsilon}_{\mathrm{m}\mathrm{i}\mathrm{n}}$.

#### 2.5. Characteristic Values for Cluster Evaluation

## 3. Results

#### 3.1. Pre-Processing of Data

_{X}emissions cannot be reduced. As a consequence, the ECU enriches the mixture to operate at $\lambda <1$ to purge the oxygen from the catalytic converter due to the oxidation of CO and HC ($\mathsf{\Delta}t\cong 10\mathrm{s}$ with voltage regaining ${U}_{\mathrm{H}\mathrm{E}\mathrm{G}\mathrm{O}}\cong 800\mathrm{m}\mathrm{V}$). This maneuver is repeated in both events. Signal $1$ and signal $2$ are to be considered equal from a technical point of view. The slight difference in the durations of the enriched and lean phases has a minor influence on the resulting emission event. Here, an unlimited DTW is useful.

#### 3.2. Verification of HDBSCAN Using Data Extract

#### 3.3. Application of HDBSCAN on the Complete Dataset

_{X}events. As a reference signal, the engine speed is used. An automated definition of the minimum cluster size ${C}_{\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{S}\mathrm{i}\mathrm{z}\mathrm{e}}$ and ${\epsilon}_{\mathrm{m}\mathrm{i}\mathrm{n}}$ is used. The definition is performed by calculating the $DBCV$ for cluster sets from ${C}_{\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{S}\mathrm{i}\mathrm{z}\mathrm{e}}=3$ to $16$. The setup that reaches the maximum $DBCV$ is used. ${\rho}_{\mathrm{m}\mathrm{i}\mathrm{n}}$ is defined as identical to ${C}_{\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{S}\mathrm{i}\mathrm{z}\mathrm{e}}$. Based on this, ${\epsilon}_{\mathrm{m}\mathrm{i}\mathrm{n}}$ is then iterated and, consistently, the value reaching the highest $DBCV$ is selected.

## 4. Discussion

#### 4.1. Evaluation Criteria and HDBSCAN Validation

#### 4.2. Pre-Processing of Data

#### 4.3. Judgement of HDBSCAN Application for Emission Calibration Purposes

_{X}emissions. These $959$ events have a total duration of $\mathrm{21,827}\mathrm{s}$. The automatic clustering, based on the engine speed signal in Section 3.3, with a total of $69$ raw clusters shows the tendency of over-classification and the formation of micro-clusters. A manual visual correction of the clusters results in $24$ final clusters. Here, automatically assigned clusters are only merged, and splitting an existing cluster is not required. Although this step required manual engineering effort, this procedure is suggested. Variations in the HDBSCAN settings show that the formation of rather large clusters is not desirable.

_{X}emission intensity of the events in the previously presented clusters. While the expected intensity of each cluster is below $0.2\mathrm{g}/\mathrm{k}\mathrm{m}$ for most clusters, clusters $2$, $10$, $11$, $12$, $13$, $17,$ and $18$ show rather high intensities. Clusters $17$ and $18$ are the clusters that summarize statistically the most intense events. Cluster $10$ and cluster $11$ contain the highest overall events considering the outliers in the boxplot intensity distribution.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## List of Abbreviations

ARI | Adjusted Rand Index |

AT | automatic transmission |

AWD | all-wheel drive |

CE | complexity estimate |

cf. | confer |

CF | complexity factor |

CO | carbon monoxide |

DBCV | Density-Based Cluster Validation |

DoE | Design-of-Experiments |

DTW | dynamic time warping |

e.g. | for example |

EATS | exhaust aftertreatment system |

ECU | engine control unit |

EDTW | complexity estimate dynamic time warping |

EiL | Engine-in-the-Loop |

FN | False Negative |

FP | False Positive |

GPF | gasoline particulate filter |

HC | hydrocarbons |

HDBSCAN | Hierarchical Density-based Spatial Clustering of Applications with Noise |

HiL | Hardware-in-the-Loop |

MiL | Model-in-the-Loop |

NOX | nitrogen oxides |

PEMS | portable emission measurement system |

PiL | Powertrain-in-the-Loop |

RDE | real driving emissions |

RI | Rand Index |

SOC | state of charge |

TN | True Negative |

TP | True Positive |

TWC | three-way catalytic converter |

ViL | Vehicle-in-the-Loop |

WLTC | Worldwide Harmonized Light Vehicles Test Cycle |

XiL | X-in-the-Loop |

## References

- Maurer, R.; Yadla, S.K.; Balazs, A.; Thewes, M.; Walter, V.; Uhlmann, T. Designing Zero Impact Emission Vehicle Concepts. In Experten-Forum Powertrain: Ladungswechsel und Emissionierung 2020; Liebl, J., Ed.; Springer: Berlin/Heidelberg, Germany, 2021; pp. 75–116. ISBN 978-3-662-63523-0. [Google Scholar]
- Mulholland, E.; Miller, J.; Bernard, Y.; Lee, K.; Rodríguez, F. The role of NOx emission reductions in Euro 7/VII vehicle emission standards to reduce adverse health impacts in the EU27 through 2050. Transp. Eng.
**2022**, 9, 100133. [Google Scholar] [CrossRef] - European Commission. The European Green Deal: Communication from the Commission to the European Parliament, the European Council, the Council, the European Economic and Social Committee and the Committee of the Regions; European Commission: Brussels, Belgium, 2019; 640p. [Google Scholar]
- Mulholland, E.; Miller, J.; Braun, C.; Jin, L.; Rodríguez, F. Quantifying the Long-Term Air Quality and Health Benefits from Euro 7/VII Standards in Europe. Int. Counc. Clean Transp.
**2021**. Available online: https://euagenda.eu/upload/publications/eu-euro7-standards-health-benefits-jun21.pdf (accessed on 1 January 2024). - Boger, T.; Rose, D.; He, S.; Joshi, A. Developments for future EU7 regulations and the path to zero impact emissions—A catalyst substrate and filter supplier’s perspective. Transp. Eng.
**2022**, 10, 100129. [Google Scholar] [CrossRef] - European Commission. Commission Regulation (EU) 2017/1151; European Commission: Brussels, Belgium, 2017. [Google Scholar]
- European Commission. Proposal for a Regulation of the European Parliament and of the Council on Type-Approval of Motor Vehicles and Engines and of Systems, Components and Separate Technical Units Intended for such Vehicles, with Respect to Their Emissions and Battery Durability (Euro 7) and Repealing Regulations (EC) No 715/2007 and (EC) No 595/2009; Proposal; European Commission: Brussels, Belgium, 2022; Volume 0365. [Google Scholar]
- Claßen, J.; Krysmon, S.; Dorscheidt, F.; Sterlepper, S.; Pischinger, S. Real Driving Emission Calibration—Review of Current Validation Methods against the Background of Future Emission Legislation. Appl. Sci.
**2021**, 11, 5429. [Google Scholar] [CrossRef] - Andert, J.; Xia, F.; Klein, S.; Guse, D.; Savelsberg, R.; Tharmakulasingam, R.; Thewes, M.; Scharf, J. Road-to-rig-to-desktop: Virtual development using real-time engine modelling and powertrain co-simulation. Int. J. Engine Res.
**2019**, 20, 686–695. [Google Scholar] [CrossRef] - Fathy, H.K.; Filipi, Z.S.; Hagena, J.; Stein, J.L. Review of hardware-in-the-loop simulation and its prospects in the automotive area. In Modeling and Simulation for Military Applications SPIE:62280E, Proceedings of the Defense and Security Symposium, Orlando, FL, USA, 17 April 2006; SPIE Proceedings; Schum, K., Sisti, A.F., Eds.; SPIE: Orlando, FL, USA; Kissimme, FL, USA, 2006. [Google Scholar]
- Lee, S.-Y.; Andert, J.; Neumann, D.; Querel, C.; Scheel, T.; Aktas, S.; Miccio, M.; Scahub, J.; Koetter, M.; Ehrly, M. Hardware-in-the-Loop-Based Virtual Calibration Approach to Meet Real Driving Emissions Requirements; SAE Technical Paper Series; SAE International: Warrendale, PA, USA, 2018. [Google Scholar]
- Filipi, Z.; Fathy, H.; Hagena, J.; Knafl, A.; Ahlawat, R.; Liu, J.; Jung, D.; Assanis, D.; Peng, H.; Stein, J. Engine-in-the-Loop Testing for Evaluating Hybrid Propulsion Concepts and Transient Emissions—HMMWV Case Study. SAE Trans.
**2006**, 115, 23–41. [Google Scholar] [CrossRef] - Gerstenberg, J.; Hartlief, H.; Tafel, S. RDE-Entwicklungsumgebung am hochdynamischen Motorprüfstand. ATZextra
**2015**, 20, 36–41. [Google Scholar] [CrossRef] - Jiang, S.; Smith, M.H.; Kitchen, J.; Ogawa, A. Development of an Engine-in-the-Loop Vehicle Simulation System in Engine Dynamometer Test Cell; SAE Technical Paper 2009-01-1039; SAE International: Warrendale, PA, USA, 2009. [Google Scholar] [CrossRef]
- Donn, C.; Zulehner, W.; Pfister, F. Realfahrtests für die Antriebsentwicklung mithilfe des virtuellen Fahrversuchs. ATZextra
**2019**, 24, 44–49. [Google Scholar] [CrossRef] - Hipp, J.; Schmidt, D.; Bauer, S.; Steinhaus, T.; Beidl, C. Methodikbaukasten zur effizienten, zielgerichteten RDE-Entwicklung—Potenziale und Perspektiven. In Simulation und Test 2018; Liebl, J., Ed.; Springer Fachmedien Wiesbaden GmbH: Wiesbaden, Germany, 2019; ISBN 978-3-658-25293-9. [Google Scholar]
- Fagcang, H.; Stobart, R.; Steffen, T. A review of component-in-the-loop: Cyber-physical experiments for rapid system development and integration. Adv. Mech. Eng.
**2022**, 14, 168781322211099. [Google Scholar] [CrossRef] - Picerno, M.; Lee, S.-Y.; Ehrly, M.; Schaub, J.; Andert, J. Virtual Powertrain Simulation: X-in-the-Loop Methods for Concept and Software Development. In 21. Internationales Stuttgarter Symposium; Bargende, M., Reuss, H.-C., Wagner, A., Eds.; Springer Fachmedien Wiesbaden GmbH: Wiesbaden, Germany, 2021; pp. 531–545. ISBN 978-3-658-33465-9. [Google Scholar]
- Wenig, M.; Artukovic, D.; Armbruster, C. vRDE—Virtual Real Driving Emission. In VPC—Simulation und Test 2016; Liebl, J., Beidl, C., Eds.; Springer Fachmedien Wiesbaden GmbH: Wiesbaden, Germany, 2017; ISBN 978-3-658-16753-0. [Google Scholar]
- Riccio, A.; Monzani, F.; Landi, M. Towards a Powerful Hardware-in-the-Loop System for Virtual Calibration of an Off-Road Diesel Engine. Energies
**2022**, 15, 646. [Google Scholar] [CrossRef] - Wu, H.; Zhang, H.; Motevalli, V.; Qian, Y.; Wolfe, A. Hybrid Electric Vehicle Powertrain Controller Development Using Hardware in the Loop Simulation; SAE Technical Paper Series; SAE International: Warrendale, PA, USA, 2013. [Google Scholar]
- Merl, R.; Kokalj, G.; Wultsch, B.; Klumaier, K.; Eberhard, F.; Ivarson, M. Innovative Lösungen zur Applikation hybrider Antriebe. In Experten-Forum Powertrain: Simulation und Test 2020; Springer: Berlin/Heidelberg, Germany, 2020; pp. 121–134. [Google Scholar] [CrossRef]
- Kuznik, A.; Steinhaus, T.; Stumpp, M.; Beidl, C. Optimierung des Emissionsverhaltens innerhalb der hybriden Betriebsstrategie am Prüfstand mittels Co-Simulation. In Experten-Forum Powertrain: Simulation und Test 2020; Springer: Berlin/Heidelberg, Germany, 2021; pp. 31–45. [Google Scholar] [CrossRef]
- Guse, D.; Andert, J.; Walter, S.; Meyer, N. Next Level of Testing—Extended Frontloading through Latency-optimized EiL Test Benches. MTZ Worldw.
**2020**, 81, 44–49. [Google Scholar] [CrossRef] - Heusch, C.; Guse, D.; Dorscheidt, F.; Claßen, J.; Fahrbach, T.; Pischinger, S.; Tegelkamp, S.; Görgen, M.; Nijs, M.; Scharf, J. Analysis of Drivability Influence on Tailpipe Emissions in Early Stages of a Vehicle Development Program by Means of Engine-in-the-Loop Test Benches; SAE Technical Paper 2020-01-0373; SAE International: Warrendale, PA, USA, 2020. [Google Scholar]
- Schmidt, H.; Buttner, K.; Prokop, G. Methods for virtual validation of automotive powertrain systems in terms of vehicle drivability—A systematic literature review. IEEE Access
**2023**, 1, 27043–27065. [Google Scholar] [CrossRef] - Mason, A.; Roberts, P.; Whelan, S.; Kondo, Y.; Brenton, L. RDE Plus—A Road to Rig Development Methodology for Complete RDE Compliance: Road to Chassis Perspective; SAE Technical Paper 2020-01-0378; SAE International: Warrendale, PA, USA, 2020. [Google Scholar]
- Roberts, P.J.; Mumby, R.; Mason, A.; Redford-Knight, L.; Kaur, P. RDE Plus—The Development of a Road, Rig and Engine-in-the-Loop Test Methodology for Real Driving Emissions Compliance; SAE Technical Paper 2019-01-0756 Series; SAE International: Warrendale, PA, USA, 2019. [Google Scholar]
- Roberts, P.; Mason, A.; Whelan, S.; Tabata, K.; Kondo, Y.; Kumagai, T.; Mumby, R.; Bates, L. RDE Plus—A Road to Rig Development Methodology for Whole Vehicle RDE Compliance: Overview; SAE Technical Paper 2020-01-0376; SAE International: Warrendale, PA, USA, 2020. [Google Scholar]
- Donateo, T.; Giovinazzi, M. Building a cycle for Real Driving Emissions. Energy Procedia
**2017**, 126, 891–898. [Google Scholar] [CrossRef] - Knopov, P.S.; Samosonok, A.S. On Markov stochastic processes with local interaction for solving some applied problems. Cybern. Syst. Anal.
**2011**, 47, 346–359. [Google Scholar] [CrossRef] - Kooijman, D.G.; Balau, A.E.; Wilkins, S.; Ligterink, N.; Cuelenaere, R. WLTP Random Cycle Generator. In Proceedings of the 2015 IEEE Vehicle Power and Propulsion Conference (VPPC), Montreal, QC, Canada, 19–22 October 2015; pp. 1–6, ISBN 978-1-4673-7637-2. [Google Scholar]
- Balau, A.E.; Kooijman, D.; Vazquez Rodarte, I.; Ligterink, N. Stochastic Real-World Drive Cycle Generation Based on a Two Stage Markov Chain Approach. SAE Int. J. Mater. Manf.
**2015**, 8, 390–397. [Google Scholar] [CrossRef] - Ashtari, A.; Bibeau, E.; Shahidinejad, S. Using Large Driving Record Samples and a Stochastic Approach for Real-World Driving Cycle Construction: Winnipeg Driving Cycle. Transp. Sci.
**2014**, 48, 170–183. [Google Scholar] [CrossRef] - Galgamuwa, U.; Perera, L.; Bandara, S. A Representative Driving Cycle for the Southern Expressway Compared to Existing Driving Cycles. Transp. Dev. Econ.
**2016**, 2, 589. [Google Scholar] [CrossRef] - Della Ragione, L.; Meccariello, G. Statistical approach to identify Naples city’s real driving cycle referring to the Worldwide harmonized Light duty Test Cycle (WLTC) framework. Sustain. Dev. Plan.
**2017**, 210, 555–566. [Google Scholar] [CrossRef] - Kondaru, M.K.; Telikepalli, K.P.; Thimmalapura, S.V.; Pandey, N.K. Generating a Real World Drive Cycle—A Statistical Approach; SAE Technical Paper 2018-01-0325; SAE International: Warrendale, PA, USA, 2018. [Google Scholar]
- Nies, H.; Beidl, C.; Hüners, H.; Fischer, K. Systematische Entwicklungsmethodik für eine robuste Motorkalibrierung unter RDE-Randbedingungen. In Experten-Forum Powertrain: Simulation und Test 2019; Springer: Berlin/Heidelberg, Germany, 2019; Volume 76, pp. 50–62. [Google Scholar] [CrossRef]
- Maschmeyer, H.; Beidl, C.; Düser, T.; Schick, B. RDE-Homologation—Herausforderungen, Lösungen und Chancen. MTZ Mot. Z
**2016**, 77, 84–91. [Google Scholar] [CrossRef] - Faubel, L.; Lensch-Franzen, C.; Schuhardt, A.; Krohn, C. Übertrag von RDE-Anforderungen in eine modellbasierte Prüfstandsumgebung. MTZ Extra
**2016**, 21, 44–49. [Google Scholar] [CrossRef] - Mayr, C.; Merl, R.; Gigerl, H.-P.; Teitzer, M.; König, D.; Stemmer, D.; Retter, F. Test emissionsrelevanter Fahrzyklen auf dem Motorprüfstand. In Simulation und Test 2018; Liebl, J., Ed.; Springer Fachmedien Wiesbaden GmbH: Wiesbaden, Germany, 2019; ISBN 978-3-658-25293-9. [Google Scholar]
- Mirfendreski, A. Powertrain Development with Artificial Intelligence: History, Work Processes, Concepts, Methods and Application Examples; Springer: Berlin/Heidelberg, Germany, 2022; ISBN 9783662638620. [Google Scholar]
- Isermann, R.; Sequenz, H. Model-based development of combustion-engine control and optimal calibration for driving cycles: General procedure and application. IFAC-PapersOnLine
**2016**, 49, 633–640. [Google Scholar] [CrossRef] - Wasserburger, A.; Hametner, C. Automated Generation of Real Driving Emissions Compliant Drive Cycles Using Conditional Probability Modeling. In Proceedings of the 2020 IEEE Vehicle Power and Propulsion Conference (VPPC), Gijon, Spain, 18 November–16 December 2020; pp. 1–6, ISBN 978-1-7281-8959-8. [Google Scholar]
- Wasserburger, A.; Didcock, N.; Hametner, C. Efficient real driving emissions calibration of automotive powertrains under operating uncertainties. Eng. Optim.
**2021**, 55, 140–157. [Google Scholar] [CrossRef] - Millo, F.; Piano, A.; Zanelli, A.; Boccardo, G.; Rimondi, M.; Fuso, R. Development of a Fully Physical Vehicle Model for Off-Line Powertrain Optimization: A Virtual Approach to Engine Calibration; SAE Technical Paper Series; SAE International: Warrendale, PA, USA, 2021. [Google Scholar]
- Arya, P.; Millo, F.; Mallamo, F. A fully automated smooth calibration generation methodology for optimization of latest generation of automotive diesel engines. Energy
**2019**, 178, 334–343. [Google Scholar] [CrossRef] - Meli, M.; Pischinger, S.; Kansagara, J.; Dönitz, C.; Liberda, N.; Nijs, M. Proof of Concept for Hardware-in-the-Loop Based Knock Detection Calibration; SAE Technical Paper 2021-01-0424; SAE International: Warrendale, PA, USA, 2021. [Google Scholar]
- Neumann, D.; Steinbach, M.; Kutzner, T.; Lehmann, A.; Kassem, V.; Dreiser, M. Model supported calibration process for future RDE requirements. In 16. Internationales Stuttgarter Symposium; Bargende, M., Reuss, H.-C., Wiedemann, J., Eds.; Springer Fachmedien Wiesbaden GmbH: Wiesbaden, Germany, 2016; pp. 565–579. ISBN 978-3-658-13254-5. [Google Scholar]
- Böhmer, M. Simulation der Abgasemissionen von Hybridfahrzeugen für Reale Fahrbedingungen. Ph.D. Dissertation, Rheinisch-Westfälische Technische Hochschule Aachen, Aachen, Germany, 2017. [Google Scholar]
- Morcinkowski, B.; Adomeit, P.; Mally, M.; Esposito, S.; Walter, V.; Yadla, S. Emissionsvorhersage in der Entwicklung ottomotorischer EU7-Antriebe. In Experten-Forum Powertrain: Ladungswechsel und Emissionierung 2019; Liebl, J., Ed.; Springer Fachmedien Wiesbaden GmbH: Wiesbaden, Germany, 2020; pp. 11–23. ISBN 978-3-658-28708-5. [Google Scholar]
- Wang, W.; Xia, F.; Nie, H.; Chen, Z.; Gong, Z.; Kong, X.; Wei, W. Vehicle Trajectory Clustering Based on Dynamic Representation Learning of Internet of Vehicles. IEEE Trans. Intell. Transport. Syst.
**2021**, 22, 3567–3576. [Google Scholar] [CrossRef] - Shi, X.; Wong, Y.D.; Chai, C.; Li, M.Z.-F.; Chen, T.; Zeng, Z. Automatic Clustering for Unsupervised Risk Diagnosis of Vehicle Driving for Smart Road. IEEE Trans. Intell. Transport. Syst.
**2022**, 23, 17451–17465. [Google Scholar] [CrossRef] - Novotny, G.; Liu, Y.; Wober, W.; Olaverri-Monreal, C. Autonomous Vehicle Calibration via Linear Optimization. In Proceedings of the 2022 IEEE Intelligent Vehicles Symposium (IV), Aachen, Germany, 4–9 June 2022; pp. 527–532, ISBN 978-1-6654-8821-1. [Google Scholar]
- Krysmon, S.; Dorscheidt, F.; Claßen, J.; Düzgün, M.; Pischinger, S. Real Driving Emissions—Conception of a Data-Driven Calibration Methodology for Hybrid Powertrains Combining Statistical Analysis and Virtual Calibration Platforms. Energies
**2021**, 14, 4747. [Google Scholar] [CrossRef] - Claßen, J.; Pischinger, S.; Krysmon, S.; Sterlepper, S.; Dorscheidt, F.; Doucet, M.; Reuber, C.; Görgen, M.; Scharf, J.; Nijs, M.; et al. Statistically supported real driving emission calibration: Using cycle generation to provide vehicle-specific and statistically representative test scenarios for Euro 7. Int. J. Engine Res.
**2020**, 21, 1783–1799. [Google Scholar] [CrossRef] - Claßen, J. Entwicklung Statistisch Relevanter Prüfszenarien zur Bewertung der Fahrzeug-Emissionsrobustheit unter Realen Fahrbedingungen. Ph.D. Dissertation, Rheinisch-Westfälische Technische Hochschule Aachen, Aachen, Germany, 2022. [Google Scholar] [CrossRef]
- Salvador, S.; Chan, P. Toward accurate dynamic time warping in linear time and space. IDA
**2007**, 11, 561–580. [Google Scholar] [CrossRef] - Serrà, J.; Arcos, J.L. An empirical evaluation of similarity measures for time series classification. Knowl. Based Syst.
**2014**, 67, 305–314. [Google Scholar] [CrossRef] - McInnes, L.; Healy, J.; Astels, S. HDBSCAN: Hierarchical density based clustering. JOSS
**2017**, 2, 205. [Google Scholar] [CrossRef] - Krysmon, S.; Claßen, J.; Pischinger, S.; Trendafilov, G.; Düzgün, M.; Dorscheidt, F. RDE Calibration—Evaluating Fundamentals of Clustering Approaches to Support the Calibration Process. Vehicles
**2023**, 5, 404–423. [Google Scholar] [CrossRef] - Petitjean, F.; Forestier, G.; Webb, G.I.; Nicholson, A.E.; Chen, Y.; Keogh, E. Faster and more accurate classification of time series by exploiting a novel dynamic time warping averaging algorithm. Knowl. Inf. Syst.
**2016**, 47, 1–26. [Google Scholar] [CrossRef] - Abanda, A.; Mori, U.; Lozano, J.A. A review on distance based time series classification. Data Min. Knowl. Disc.
**2019**, 33, 378–412. [Google Scholar] [CrossRef] - Rani, S.; Sikka, G. Recent Techniques of Clustering of Time Series Data: A Survey. IJCA
**2012**, 52, 1–9. [Google Scholar] [CrossRef] - Jung, Y.; Park, H.; Du, D.-Z.; Drake, B.L. A Decision Criterion for the Optimal Number of Cluster in Hierarchical Clustering. J. Glob. Optim.
**2003**, 25, 91–111. [Google Scholar] [CrossRef] - Na, S.; Xumin, L.; Yong, G. Research on k-means Clustering Algorithm: An Improved k-means Clustering Algorithm. In Proceedings of the 2010 Third International Symposium on Intelligent Information Technology and Security Informatics (IITSI), Ji’an, China, 2–4 April 2010; pp. 63–67, ISBN 978-1-4244-6730-3. [Google Scholar]
- Ahmed, M.; Seraj, R.; Islam, S.M.S. The k-means Algorithm: A Comprehensive Survey and Performance Evaluation. Electronics
**2020**, 9, 1295. [Google Scholar] [CrossRef] - Wiedenbeck, M.; Züll, C. Klassifikation mit Clusteranalyse: Grundlegende Techniken Hierarchischer und K-Means-Verfahren. GESIS-How-to(10). 2001. Available online: https://nbn-resolving.org/urn:nbn:de:0168-ssoar-201428 (accessed on 1 January 2024).
- Rousseeuw, P.J. Silhouettes: A graphical aid to the interpretation and validation of cluster analysis. J. Comput. Appl. Math.
**1987**, 20, 53–65. [Google Scholar] [CrossRef] - Moulavi, D.; Jaskowiak, P.A.; Campello, R.J.G.B.; Zimek, A.; Sander, J. Density-Based Clustering Validation. In Proceedings of the 14th SIAM International Conference on Data Mining (SDM), Philadelphia, PA, USA, 24–26 April 2014; pp. 839–847. [Google Scholar] [CrossRef]
- Davies, D.L.; Bouldin, D.W. A Cluster Separation Measure. IEEE Trans. Pattern Anal. Mach. Intell.
**1979**, PAMI-1, 224–227. [Google Scholar] [CrossRef] - Rand, W.M. Objective Criteria for the Evaluation of Clustering Methods. J. Am. Stat. Assoc.
**1971**, 66, 846. [Google Scholar] [CrossRef] - Steinley, D. Properties of the Hubert-Arabie adjusted Rand index. Psychol. Methods
**2004**, 9, 386–396. [Google Scholar] [CrossRef] - Batista, G.E.A.P.A.; Wang, X.; Keogh, E.J. A Complexity-Invariant Distance Measure for Time Series. In Proceedings of the Eleventh SIAM International Conference on Data Mining, SDM 2011, Mesa, AZ, USA, 28–30 April 2011; pp. 699–710. [Google Scholar] [CrossRef]
- Petitjean, F.; Ketterlin, A.; Gançarski, P. A global averaging method for dynamic time warping, with applications to clustering. Pattern Recognit.
**2011**, 44, 678–693. [Google Scholar] [CrossRef]

Characteristic | Unit | Value |
---|---|---|

Vehicle weight | $\mathrm{k}\mathrm{g}$ | $>2000$ |

Fuel | $-$ | Gasoline |

Engine type | $-$ | Turbo-charged 8 cylinder |

Engine power and torque | $\mathrm{k}\mathrm{W}$/$\mathrm{N}\mathrm{m}$ | $>400$/$>600$ |

Cubic capacity | $\mathrm{c}{\mathrm{m}}^{3}$ | $~4000$ |

Transmission | $-$ | Automatic Transmission (AT) |

Drivetrain | $-$ | All-wheel drive (AWD) |

Exhaust aftertreatment system (EATS) | $-$ | Three-way catalytic converter (TWC) and gasoline particulate filter (GPF) |

Condition of EATS | $-$ | Stabilized EATS ($~70\%$) and aged EATS ($~30\%$) |

Emission target | $-$ | EU6d |

Signal | Unit | Urban | Rural | Motorway |
---|---|---|---|---|

Speed breakpoints | $\mathrm{k}\mathrm{m}/\mathrm{h}$ | $0$ | $80$ | $160$ |

Intensity breakpoints | $\mathrm{m}\mathrm{g}/\mathrm{k}\mathrm{m}$ | $30$ | $30$ | $30$ |

Signal | Events Used | Reference Clusters Defined |
---|---|---|

Engine speed | $366$ | $7$ |

Vehicle speed | $448$ | $29$ |

Flag fuel cut-off | $648$ | $16$ |

Relative air charge | $304$ | $18$ |

Pedal position | $271$ | $23$ |

Voltage of two-point downstream lambda sensor | $725$ | $10$ |

Engine torque | $494$ | $43$ |

Relative fuel mass | $461$ | $36$ |

Catalytic converter temperature | $885$ | $11$ |

Exhaust gas mass flow | $174$ | $12$ |

Actual ignition angle | $237$ | $15$ |

Optimal ignition angle | $561$ | $30$ |

Signal | Identified Clusters | Outliers | $\mathit{A}\mathit{R}\mathit{I}$ | $\mathit{D}\mathit{B}\mathit{C}\mathit{V}$ |
---|---|---|---|---|

Engine speed | $8$ | $20$ | $0.68$ | $0.57$ |

Vehicle speed | $10$ | $8$ | $0.85$ | $0.63$ |

Flag fuel cut-off | $61$ | $24$ | $0.7$ | $1.00$ |

Relative air charge | $22$ | $5$ | $0.99$ | $0.52$ |

Pedal position | $22$ | $16$ | $0.71$ | $0.47$ |

Voltage of two-point downstream lambda sensor | $19$ | $27$ | $0.62$ | $0.49$ |

Engine torque | $27$ | $36$ | $0.78$ | $0.50$ |

Relative fuel mass | $28$ | $16$ | $0.82$ | $0.44$ |

Catalytic converter temperature | $11$ | $1$ | $0.50$ | $0.68$ |

Exhaust gas mass flow | $14$ | $3$ | $0.71$ | $0.62$ |

Actual ignition angle | $17$ | $19$ | $0.80$ | $0.48$ |

Optimal ignition angle | $22$ | $43$ | $0.69$ | $0.40$ |

**Table 5.**Parameters and results of clustering iterations for the engine speed signal of NO

_{X}events.

Loop 1 | Loop 2 | Loop 3 | Loop 4 | ||
---|---|---|---|---|---|

Number of events | - | 959 | 448 | 203 | 159 |

${C}_{\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{S}\mathrm{i}\mathrm{z}\mathrm{e}}$ | - | 4 | 3 | 5 | 3 |

${\epsilon}_{\mathrm{m}\mathrm{i}\mathrm{n}}$ | % | 1 | 1 | 1 | 1 |

Resulting clusters | - | 47 | 15 | 4 | 3 |

Detected outliers | - | 448 | 203 | 159 | 77 |

$DBCV$ | - | 0.589 | 0.495 | 0.303 | 0.403 |

Average Silhouette Score | - | 0.26 | 0.23 | 0.1 | 0.13 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Krysmon, S.; Pischinger, S.; Claßen, J.; Trendafilov, G.; Düzgün, M.; Dorscheidt, F.; Nijs, M.; Görgen, M.
Applying Density-Based Clustering for the Analysis of Emission Events in Real Driving Emissions Calibration. *Future Transp.* **2024**, *4*, 46-66.
https://doi.org/10.3390/futuretransp4010004

**AMA Style**

Krysmon S, Pischinger S, Claßen J, Trendafilov G, Düzgün M, Dorscheidt F, Nijs M, Görgen M.
Applying Density-Based Clustering for the Analysis of Emission Events in Real Driving Emissions Calibration. *Future Transportation*. 2024; 4(1):46-66.
https://doi.org/10.3390/futuretransp4010004

**Chicago/Turabian Style**

Krysmon, Sascha, Stefan Pischinger, Johannes Claßen, Georgi Trendafilov, Marc Düzgün, Frank Dorscheidt, Martin Nijs, and Michael Görgen.
2024. "Applying Density-Based Clustering for the Analysis of Emission Events in Real Driving Emissions Calibration" *Future Transportation* 4, no. 1: 46-66.
https://doi.org/10.3390/futuretransp4010004