# A Mixed Ensemble Learning and Time-Series Methodology for Category-Specific Vehicular Energy and Emissions Modeling

^{*}

## Abstract

**:**

## 1. Introduction

_{2}) rates by 17% and 35%, respectively. A dramatic overestimation (up to 420%) was observed for Nitrogen Oxides (NO

_{x}) and Particulate Matters (PM) predictions as well.

- (1)
- To achieve acceptable prediction accuracies in the absence of precise engine-state measurements (a requirement for instrument-independent models) while addressing the serial correlation and the lagged impact of variables on FCR and ERs, we utilize a state-of-the-art Machine Learning (ML) technique of Recurrent Neural Networks (RNN) to keep the models’ architecture in alignment with the nature of the observed vehicular operation data.
- (2)
- The fact that the order of lagged effects of variables on FCR and ERs is not necessarily constant has never been questioned in the literature. Hence, we use an Ensemble Learning (EL) approach to tackle such uncertainty and dynamicity.
- (3)
- Unlike the vast majority of the previous studies that are confined to vehicle-specific modeling, we consider the need for category-specific FCR and ER models; hence, we introduce a generalization methodology (from vehicles to categories) founded upon well-recognized forecast-combination techniques.

## 2. Literature Review

_{x}formation in the combustion chamber are calculated by injecting IEV measurements into the Zeldovich model [23,24] and the resulting estimates are used to predict the NO

_{x}rate [3].

## 3. Methodology

#### 3.1. On-Road Experiments

_{2}, PM, Nitrogen Monoxide (NO), and Nitrogen Dioxide (NO

_{2}) concentrations.

_{2}using Non-Dispersive Infra-Red (NDIR) absorption technology with a measurement range of 0–20% and an accuracy of ±70 ppm. For the NO

_{x}, 3-electrode electrochemical sensors capable of measuring up to 5000 ppm for NO and 300 ppm for NO

_{2}were incorporated. The measurement resolution for NO and NO

_{2}were 1–5 ppm and 0.1 ppm, respectively. Regarding PM, the unit measures undiluted emissions through the response of three dissimilar particulate sensors. Ionization was used for ultra-fine/fine particulates usually between 0.01 to 1 micron, while a combination of opacimeter and laser scattering was deployed for coarse particulates up to 10 microns.

#### 3.2. Data Preparation

_{2}, ppm for NO

_{x}, and $\mathrm{micrograms}/{\mathrm{m}}^{3}$ for particulate matters. To convert second-by-second concentrations into temporal rates in the absence of exhaust flow rate data, an all-in all-out assumption was made (ignoring the existence of minor leakage from the engine to the exhaust pipe) and the MAF rate was used as an alternative to the exhaust flow rate. However, the exhaust-pipe lag (due to its length and presence of resonators and catalytic converter) could introduce errors to the calculations. Later in this section, an RNN modeling approach is described as a solution for capturing such lagged effects.

_{2}, NO

_{2}, and NO, respectively.

#### 3.3. Vehicle-Specific RNN Modeling

#### 3.4. Primary Forecast Combination for Lag-Specific RNNs

#### 3.5. Category-Specific Ensemble Modeling

^{th}vehicle at all. Each of the category members would play the role of left-out-vehicle once. As a result, the out-of-sample validation is repeated n times and the average of the validation scores is finally used for evaluating the prediction power of the supermodel.

## 4. Results and Discussion

#### 4.1. Metamodel Development Results

_{2}-rate meta-modeling, whereas the much simpler method of Linear Regression led to the best results for NO

_{2}, NO, and PM rates.

_{2}rates. Hence, only more sophisticated EL algorithms could extract underlying nonlinear dependencies and achieve considerable improvements. It is noteworthy that the 28%, 23%, and 16% improvement records in RMSE, when comparing the metamodel score with the score of the best component model, are all dedicated to FCR and CO

_{2}rate metamodels (an average of 6% improvement was achieved in this group of metamodels). Such high improvements confirm the existence of higher-level nonlinear dependencies that the lag-specific RNNs were incapable of capturing them alone.

_{2}, and PM are varied enough and as inputs to metamodels, they possess such linear correlations with the dependent which allows forecast combinations such as simple unregularized linear regression algorithm to work efficiently and even lead to score improvements. The average improvement for the discussed emissions is equal to 2%. The lower average improvement in RMSE score compared to FCR and CO

_{2}metamodels could be due to the dominant effect of one lag-specific component model on the metamodel performance. A possible interpretation is that for NO

_{x}and PM emissions, the existence of a relatively constant lag order is feasible, while for fuel and CO

_{2}, distributively lagged effects exist.

_{2}rate.

_{x}and PM, despite the higher level of prediction error, the metamodel outperforms the lag-specific component models. In Figure 11, the true observations are compared to the metamodel predictions for all data points corresponding to the same three vehicles-dependent pairs presented in Figure 10.

#### 4.2. Validating Metamodels

_{2}and linear regression for NO

_{x}and PM) are directly applied on data (by skipping the RNN modeling step) and the modeling scores are compared to that of the metamodels. By this comparison, we look to emphasize the impact of mixed modeling methodology (mixture of EL and RNN techniques) in achieving outstanding RMSE scores and to prove that use of meta-regressors alone would not be enough to achieve such scores. As shown in Figure 12, the metamodels outperformed the direct models for all vehicle-dependent pairs with an average margin of 13% (and a maximum of 38%) regarding the RMSE score. Only for 8 out of 103 vehicle-dependent pairs (most of which corresponding to NO), the direct model has scored a lower RMSE value. Such few outliers were expected as our NO-metamodels were already among the weakest compared to the fuel and other emissions.

#### 4.3. Supermodel Development Results

_{2}generation is expectable. However, this criterion does not seem appropriate for NO and PM emissions where limited improvements is achieved.

_{x}emission rates are generally so low in gasoline-engine vehicles, even minor sensor errors affect the readings considerably.

_{2}rate, while similar to the metamodels, Linear and Ridge Regressions shoulder the forecast combination burden of NO

_{x}and PM supermodels better.

_{2}rates, R-squared scores of 0.95 and 0.88 are achieved, respectively. The method has made acceptable predictions for NO

_{2}as well, although it appears to be weak in capturing peaks. Nevertheless, as our categorization process still requires refinement, an R-squared score of 0.7 seems a satisfying score at this stage.

## 5. Conclusions and Future Work

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Bifulco, G.N.; Galante, F.; Pariota, L.; Spena, M.R. A Linear Model for the Estimation of Fuel Consumption and the Impact Evaluation of Advanced Driving Assistance Systems. Sustainability
**2015**, 7, 14326–14343. [Google Scholar] [CrossRef] [Green Version] - Çapraz, A.G.; Özel, P.; Sevkli, M.; Beyca Ömer, F. Fuel Consumption Models Applied to Automobiles Using Real-time Data: A Comparison of Statistical Models. Procedia Comput. Sci.
**2016**, 83, 774–781. [Google Scholar] [CrossRef] [Green Version] - Frey, H.C.; Zhang, K.; Rouphail, N. Vehicle-Specific Emissions Modeling Based upon on-Road Measurements. Environ. Sci. Technol.
**2010**, 44, 3594–3600. [Google Scholar] [CrossRef] [PubMed] - Nie, Y.; Li, Q. An eco-routing model considering microscopic vehicle operating conditions. Transp. Res. Part B Methodol.
**2013**, 55, 154–170. [Google Scholar] [CrossRef] - Rakha, H.A.; Ahn, K.; Moran, K.; Saerens, B.; Van Den Bulck, E. Virginia Tech Comprehensive Power-Based Fuel Consumption Model: Model development and testing. Transp. Res. Part D Transp. Environ.
**2011**, 16, 492–503. [Google Scholar] [CrossRef] - Saerens, B.; Rakha, H.; Ahn, K.; Bulck, E.V.D. Assessment of Alternative Polynomial Fuel Consumption Models for Use in Intelligent Transportation Systems Applications. J. Intell. Transp. Syst.
**2012**, 17, 294–303. [Google Scholar] [CrossRef] - Zhou, Q.; Gullitti, A.; Xiao, J.; Huang, Y. Neural network-based modeling and optimization for effective vehicle emission testing and engine calibration. Chem. Eng. Commun.
**2008**, 195, 706–720. [Google Scholar] [CrossRef] - Koupal, J.; Cumberworth, M.; Michaels, H.; Beardsley, M.; Brzezinski, D. Design and Implementation of MOVES: EPA’s New Generation Mobile Source Emission Model. Int. Emiss. Invent. Conf.
**2003**, 1001, 105. [Google Scholar] - Scora, G.; Barth, M. Comprehensive Modal Emissions Model (CMEM), Version 3.01 User’s Guide; University of California: Riverside, CA, USA, 2006; p. 1070. [Google Scholar]
- Guensler, R.; Liu, H.; Xu, X.; Xu, Y.; Rodgers, M.O. MOVES-Matrix: Setup, implementation, and application. In Proceedings of the 95th Annual Meeting of the Transportation Research Board, Washington, DC, USA, 10–14 January 2016. [Google Scholar]
- Ntziachristos, L.; Gkatzoflias, D.; Kouridis, C.; Samaras, Z. COPERT: A European Road Transport Emission Inventory Model. In Information Technologies in Environmental Engineering; Springer: Berlin/Heidelberg, Germany, 2009; pp. 491–504. [Google Scholar]
- Stockholm Environment Institute. Low Emissions Analysis Platform (LEAP). 2020. Available online: https://leap.sei.org/default.asp?action=home (accessed on 22 September 2021).
- Moradi, E.; Miranda-Moreno, L. On-road vs. Software-based Measurements: On Validity of Fuel, CO
_{2}, NO_{x}, and PM Predictions by US EPA’s MOVES. In Proceedings of the Transportation Research Board 100th Annual Meeting, Washington, DC, USA, 9–13 January 2021. [Google Scholar] - Duarte, G.; Gonçalves, G.; Baptista, P.; Farias, T. Establishing bonds between vehicle certification data and real-world vehicle fuel consumption—A Vehicle Specific Power approach. Energy Convers. Manag.
**2015**, 92, 251–265. [Google Scholar] [CrossRef] - Kayes, D.; Hochgreb, S. Mechanisms of Particulate Matter Formation in Spark-Ignition Engines. 3. Model of PM Formation. Environ. Sci. Technol.
**1999**, 33, 3978–3992. [Google Scholar] [CrossRef] - Zhai, H.; Frey, H.C.; Rouphail, N. A Vehicle-Specific Power Approach to Speed- and Facility-Specific Emissions Estimates for Diesel Transit Buses. Environ. Sci. Technol.
**2008**, 42, 7985–7991. [Google Scholar] [CrossRef] [PubMed] - Moradi, E.; Miranda-Moreno, L. Vehicular fuel consumption estimation using real-world measures through cascaded machine learning modeling. Transp. Res. Part D Transp. Environ.
**2020**, 88, 102576. [Google Scholar] [CrossRef] - Arrègle, J.; López, J.J.; Guardiola, C.; Monin, C. Sensitivity Study of a NOx Estimation Model for On-Board Applications; SAE International: Washington, DC, USA, 2008. [Google Scholar]
- Demesoukas, S. 0D/1D Combustion Modeling for the Combustion Systems Optimization of Spark Ignition Engines; Université d′Orléans: Montpellier, France, 2015. [Google Scholar]
- Payri, F.; Arrègle, J.; López, J.J.; Mocholí, E. Diesel NOx Modeling with a Reduction Mechanism for the Initial NOx Coming from EGR or Re-Entrained Burned Gases; SAE International: Warrendale, PA, USA, 2008. [Google Scholar]
- Saerens, B.; Diehl, M.; Bulck, E.V.D. Optimal Control Using Pontryagin’s Maximum Principle and Dynamic Programming. In Automotive Model Predictive Control; Springer: Berlin/Heidelberg, Germany, 2010; pp. 119–138. [Google Scholar] [CrossRef]
- Tauzia, X.; Karaky, H.; Maiboom, A. Evaluation of a semi-physical model to predict NOx and soot emissions of a CI automotive engine under warm-up like conditions. Appl. Therm. Eng.
**2018**, 137, 521–531. [Google Scholar] [CrossRef] - Anetor, L.; Odetunde, C.; Osakue, E.E. Computational Analysis of the Extended Zeldovich Mechanism. Arab. J. Sci. Eng.
**2014**, 39, 8287–8305. [Google Scholar] [CrossRef] - Blauwens, J.; Smets, B.; Peeters, J. Mechanism of “prompt” no formation in hydrocarbon flames. Symp. Combust.
**1977**, 16, 1055–1064. [Google Scholar] [CrossRef] - Rakha, H.A.; Ahn, K.; Faris, W.; Moran, K.S. Simple Vehicle Powertrain Model for Modeling Intelligent Vehicle Applications. IEEE Trans. Intell. Transp. Syst.
**2012**, 13, 770–780. [Google Scholar] [CrossRef] - Du, Y.; Wu, J.; Yang, S.; Zhou, L. Predicting vehicle fuel consumption patterns using floating vehicle data. J. Environ. Sci.
**2017**, 59, 24–29. [Google Scholar] [CrossRef] - Kim, D.; Lee, J. Application of Neural Network Model to Vehicle Emissions. Int. J. Urban Sci.
**2010**, 14, 264–275. [Google Scholar] [CrossRef] - Li, Q.; Qiao, F.; Yu, L. A Machine Learning Approach for Light-Duty Vehicle Idling Emission Estimation Based on Real Driving and Environmental Information. Environ. Pollut. Clim. Change
**2017**, 1, 106. [Google Scholar] [CrossRef] - Wu, J.-D.; Liu, J.-C. A forecasting system for car fuel consumption using a radial basis function neural network. Expert Syst. Appl.
**2012**, 39, 1883–1888. [Google Scholar] [CrossRef] - Ajtay, D.; Weilenmann, M. Static and dynamic instantaneous emission modelling. Int. J. Environ. Pollut.
**2004**, 22, 226–239. [Google Scholar] [CrossRef] - Jaikumar, R.; Nagendra, S.S.; Sivanandan, R. Modeling of real time exhaust emissions of passenger cars under heterogeneous traffic conditions. Atmos. Pollut. Res.
**2017**, 8, 80–88. [Google Scholar] [CrossRef] - Adhikari, R. A neural network based linear ensemble framework for time series forecasting. Neurocomputing
**2015**, 157, 231–242. [Google Scholar] [CrossRef] - Bianchi, F.M.; Maiorino, E.; Kampffmeyer, M.C.; Rizzi, A.; Jenssen, R. An overview and comparative analysis of recurrent neural networks for short term load forecasting. arXiv
**2017**, arXiv:1705.04378. [Google Scholar] - Kourentzes, N.; Barrow, D.K.; Crone, S.F. Neural network ensemble operators for time series forecasting. Expert Syst. Appl.
**2014**, 41, 4235–4244. [Google Scholar] [CrossRef] [Green Version] - Kang, D.; Lv, Y.; Chen, Y.-Y. Short-term traffic flow prediction with LSTM recurrent neural network. In Proceedings of the 2017 IEEE 20th International Conference on Intelligent Transportation Systems (ITSC), Yokohama, Japan, 16–19 October 2017; IEEE Press: Piscataway, NJ, USA, 2017; pp. 1–6. [Google Scholar]
- Lee, Y.-J.; Min, O. Long Short-Term Memory Recurrent Neural Network for Urban Traffic Prediction: A Case Study of Seoul. In Proceedings of the 2018 21st International Conference on Intelligent Transportation Systems (ITSC), Maui, HI, USA, 4–7 November 2018; IEEE Press: Piscataway, NJ, USA, 2018; pp. 1279–1284. [Google Scholar]
- Han, S.; Zhang, F.; Xi, J.; Ren, Y.; Xu, S. Short-term vehicle speed prediction based on Convolutional bi-directional LSTM networks. In Proceedings of the 2019 IEEE Intelligent Transportation Systems Conference (ITSC), Auckland, New Zealand, 27–30 October 2019; pp. 4055–4060. [Google Scholar]
- Wang, H.; Luo, H.; Zhao, F.; Qin, Y.; Zhao, Z.; Chen, Y. Detecting transportation modes with low-power-consumption sensors using recurrent neural network. In Proceedings of the 2018 IEEE SmartWorld, Ubiquitous Intelligence & Computing, Advanced & Trusted Computing, Scalable Computing & Communications, Cloud & Big Data Computing, Internet of People and Smart City Innovation (SmartWorld/SCALCOM/UIC/ATC/CBDCom/IOP/SCI), Guangzhou, China, 8–12 October 2018; pp. 1098–1105. [Google Scholar]
- Luo, D.; Lu, J.; Guo, G. Road Anomaly Detection Through Deep Learning Approaches. IEEE Access
**2020**, 8, 117390–117404. [Google Scholar] [CrossRef] - Bai, M.; Lin, Y.; Ma, M.; Wang, P. Travel-Time Prediction Methods: A Review. In Proceedings of the 3rd International Conference on Smart Computing and Communication, Tokyo, Japan, 10–12 December 2018; pp. 67–77. [Google Scholar]
- Duan, Y.; Yisheng, L.V.; Wang, F.-Y. Travel time prediction with LSTM neural network. In Proceedings of the 2016 IEEE 19th International Conference on Intelligent Transportation Systems (ITSC), Rio de Janeiro, Brazil, 1–4 November 2016; IEEE Press: Piscataway, NJ, USA, 2016; pp. 1053–1058. [Google Scholar]
- Jakteerangkool, C.; Muangsin, V. Short-Term Travel Time Prediction from GPS Trace Data using Re-current Neural Networks. In Proceedings of the 2020 Asia Conference on Computers and Communications (ACCC), Singapore, 4–6 December 2020; pp. 62–66. [Google Scholar]
- Lee, E.H.; Kho, S.-Y.; Kim, D.-K.; Cho, S.-H. Travel time prediction using gated recurrent unit and spatio-temporal algorithm. Proc. Inst. Civ. Eng.-Munic. Eng.
**2021**, 174, 88–96. [Google Scholar] [CrossRef] - Liu, Y.; Wang, Y.; Yang, X.; Zhang, L. Short-term travel time prediction by deep learning: A comparison of different LSTM-DNN models. In Proceedings of the 2017 IEEE 20th International Conference on Intelligent Transportation Systems (ITSC), Yokohama, Japan, 16–19 October 2017; Available online: https://ieeexplore.ieee.org/document/8317886 (accessed on 15 September 2021).
- Ran, X.; Shan, Z.; Fang, Y.; Lin, C. An LSTM-based method with attention mechanism for travel time prediction. Sensors
**2019**, 19, 861. [Google Scholar] [CrossRef] [Green Version] - Zhao, J.; Gao, Y.; Qu, Y.; Yin, H.; Liu, Y.; Sun, H. Travel Time Prediction: Based on Gated Recurrent Unit Method and Data Fusion. IEEE Access
**2018**, 6, 70463–70472. [Google Scholar] [CrossRef] - Kanarachos, S.; Mathew, J.; Fitzpatrick, M.E. Instantaneous vehicle fuel consumption estimation using smartphones and recurrent neural networks. Expert Syst. Appl.
**2019**, 120, 436–447. [Google Scholar] [CrossRef] - Jose, V.R.; Winkler, R.L. Simple robust averages of forecasts: Some empirical results. Int. J. Forecast.
**2008**, 24, 163–169. [Google Scholar] [CrossRef] - Wu, M. Trimmed and Winsorized Estimators; Michigan State University: East Lansing, MI, USA, 2006. [Google Scholar]
- Chan, L.-W. Weighted least square ensemble networks. In Proceedings of the IJCNN’99—International Joint Conference on Neural Networks, Washington, DC, USA, 10–16 July 1999. [Google Scholar]
- Ferreira, W.G.; Serpa, A.L. Ensemble of metamodels: The augmented least squares approach. Struct. Multidiscip. Optim.
**2016**, 53, 1019–1046. [Google Scholar] [CrossRef] - Hansen, B.E. Least-squares forecast averaging. J. Econ.
**2008**, 146, 342–350. [Google Scholar] [CrossRef] [Green Version] - Ren, Y.; Zhang, L.; Suganthan, P. Ensemble Classification and Regression-Recent Developments, Applications and Future Directions. IEEE Comput. Intell. Mag.
**2016**, 11, 41–53. [Google Scholar] [CrossRef] - Sagi, O.; Rokach, L. Ensemble learning: A survey. WILEY Interdiscip. Rev. Data Min. Knowl. Discov.
**2018**, 8, e1249. [Google Scholar] [CrossRef] - Agamennoni, G.; Nieto, J.I.; Nebot, E. An outlier-robust Kalman filter. In Proceedings of the 2011 IEEE International Conference on Robotics and Automation, Shanghai, China, 9–13 May 2011; pp. 1551–1558. [Google Scholar]
- Press, W.; Teukolsky, S.A. Savitzky-Golay Smoothing Filters. Comput. Phys.
**1990**, 4, 669. [Google Scholar] [CrossRef] - Lambda and Engine Performance. Available online: https://x-engineer.org/automotive-engineering/internal-combustion-engines/performance/air-fuel-ratio-lambda-engine-performance/ (accessed on 18 October 2021).
- Che, Z.; Purushotham, S.; Cho, K.; Sontag, D.; Liu, Y. Recurrent Neural Networks for Multivariate Time Series with Missing Values. Sci. Rep.
**2018**, 8, 6085. [Google Scholar] [CrossRef] [Green Version] - Gers, F.A.; Schmidhuber, J.; Cummins, F. Learning to Forget: Continual Prediction with LSTM. Neural Comput.
**2000**, 12, 2451–2471. [Google Scholar] [CrossRef] [PubMed] - Hochreiter, S.; Schmidhuber, J. Long short-term memory. Neural Comput.
**1997**, 9, 1735–1780. [Google Scholar] [CrossRef] - Lipton, Z.C.; Berkowitz, J.; Elkan, C. A Critical Review of Recurrent Neural Networks for Sequence Learning. arXiv
**2015**, arXiv:1506.00019. [Google Scholar] - Alcan, G.; Yilmaz, E.; Unel, M.; Aran, V.; Yilmaz, M.; Gurel, C.; Koprubasi, K. Estimating Soot Emission in Diesel Engines Using Gated Recurrent Unit Networks. IFAC-PapersOnLine
**2019**, 52, 544–549. [Google Scholar] [CrossRef] - Chung, J.; Gulcehre, C.; Cho, K.; Bengio, Y. Gated feedback recurrent neural networks. In Proceedings of the 32nd International Conference on Machine Learning, Lille, France, 6–11 July 2015. [Google Scholar]
- Abadi, M.; Barham, P.; Chen, J.; Chen, Z.; Davis, A.; Dean, J.; Devin, M.; Ghemawat, S.; Irving, G.; Isard, M.; et al. TensorFlow: A system for large-scale machine learning. In Proceedings of the 12th USENIX Symposium on Operating Systems Design and Implementation, Savannah, GA, USA, 2–4 November 2016. [Google Scholar]
- Pedregosa, F.; Varoquaux, G.; Gramfort, A.; Michel, V.; Thirion, B.; Grisel, O.; Blondel, M.; Prettenhofer, P.; Weiss, R.; Dubourg, V. Scikit-learn: Machine learning in Python. J. Mach. Learn. Res.
**2011**, 12, 2825–2830. [Google Scholar] - Behan, M.; Moradi, E.; Miranda-Moreno, L. A Comparative Analysis of the Vehicular Emissions Generated as a Results of Different Intersection Controls. In Proceedings of the Transportation Research Board 99th Annual Meeting, Washington, DC, USA, 12–16 January 2020. [Google Scholar]
- Jimenez-Palacios, J.L. Understanding and Quantifying Motor Vehicle Emissions with Vehicle Specific Power and TILDAS Remote Sensing. Ph.D. Thesis, Massachusetts Institute of Technology, Cambridge, MA, USA, 1998. [Google Scholar]

**Figure 2.**The aggregated trajectory of experiments in Montreal (

**left**) and Bucaramanga (

**right**) in form of a heatmap.

**Figure 4.**The (

**a**) Simple, (

**b**) LSTM, and (

**c**) GRU structures of RNN cells as well as a (

**d**) stacked many-to-one RNN architecture with lag order of p (RNN cells shown in green color).

**Figure 5.**Average normalized RMSE scores considering different RNN settings for FCR (

**top**), CO

_{2}(

**middle**), and PM (

**bottom**).

**Figure 6.**RNN predictions for lag orders of 1 and 6 for FCR, NO

_{2}, and PM rates (corresponding to three sample vehicles).

**Figure 8.**The two-stage EL approach for category-specific modeling (all the n vehicles as well as the validation vehicle correspond to one category).

**Figure 9.**Share of different ensemble estimators leading to best RMSE score when applied for different vehicles for modeling each of the dependent variables (FCR and ERs). Note that the horizontal axis shows the absolute number of vehicle-specific models.

**Figure 10.**Sample time-windows showing the prediction power of vehicle-specific metamodels in comparison with the lag-specific component models for three sample vehicle-dependent pairs.

**Figure 11.**A scatter-plot for comparing the true observation and metamodel predictions regarding the three vehicle-dependent pairs visualized in time-series format in Figure 10.

**Figure 12.**The percentage difference of the RMSE score between vehicle-specific metamodels and the direct models for all the vehicles under study.

**Figure 13.**Sample time-windows comparing the prediction power of the metamodel to true observations as well as predictions by the benchmark model (VT-CPFM).

**Figure 14.**Share of different ensemble estimators leading to best RMSE score when applied for different categories for modeling each of the dependent variables (FCR and ERs). Note that the horizontal axis shows the absolute number of category-specific models.

**Figure 15.**Random sample time-windows showing the prediction power of supermodels for 3 different category-dependent pairs.

**Figure 16.**Comparison between true observation and supermodel predictions for three selected category-dependent pairs.

Attribute | City | ||
---|---|---|---|

Montreal | Bucaramanga | Tehran | |

Total Trip Length (km) | 1804 | 291 | 255 |

Total Trip Time (Minutes) | 5224 | 825 | 444 |

Number of Test Vehicles | 22 | 7 | 6 |

Criterion | Category | Count |
---|---|---|

Vehicle Segments | SUV | 8 |

Sedan | 19 | |

Van | 1 | |

Hatchback | 7 | |

Engine Types | Regular | 31 |

Turbo-Charged | 4 | |

Transmission Types | Manual | 6 |

Automatic | 19 | |

Dual-Clutch (Auto) | 2 | |

CVT (Auto) | 8 |

Algorithm | Settings | |
---|---|---|

Attribute | Value | |

Linear Regression | Feature Scaling * | Active |

Ridge Regression | Regularization Strength | $\alpha $ = {0.1, 1.0} |

Support Vector Regression (SVR) | Kernel | Radial Basis Function (RBF) |

Gamma | Scale | |

Epsilon | 0.1 | |

Regularization Parameter | C = {1.0, 10.0} | |

Decision Tree | Splitting Criterion | Mean Squared Error (MSE) |

Splitting Strategy at Nodes | {Best, Random} | |

Maximum Tree Depth | Unbounded | |

Gradient Boosting | Loss Function | Least Squares Regression |

Splitting Criterion | Mean Squared Error (MSE) | |

Learning Rate | 0.1 | |

Number of Boosting Stages | {10, 100} | |

AdaBoost | Base Estimator | Decision Tree Regressor |

Loss Function | Linear | |

Learning Rate | 1.0 | |

Number of Boosting Stages | {10, 100} | |

Random Forest | Number of Trees | {10, 100} |

Splitting Criterion | Mean Squared Error (MSE) | |

Maximum Forest Depth | Unbounded | |

Fully-Connected ANN | Number of Hidden Layers | {1, 2} |

Layer Size (No. of Neurons) | 100 | |

Activation Function | ReLU | |

Optimizer | Adam | |

Learning Rate | 0.001 | |

Maximum No. of Iterations | 200 |

Vehicle | Model Score (R-Squared) | |
---|---|---|

Metamodel | VT-CPFM | |

Hyundai Elantra GT 2019 (2.0 L Auto) | 0.72 | 0.57 |

Chevrolet Captiva 2010 (2.4 L Auto) | 0.86 | 0.26 |

Chevrolet Cruze 2011 (1.8 L Manual) | 0.77 | 0.52 |

Vehicle | Temporal Scale/Model Type | |||||
---|---|---|---|---|---|---|

1-s | 5-s | 10-s | ||||

ARIMA | Metamodel | ARIMA | Metamodel | ARIMA | Metamodel | |

Hyundai Elantra GT 2019 (2.0 L Auto) | 0.53 | 0.69 | 0.66 | 0.83 | 0.71 | 0.84 |

Chevrolet Captiva 2010 (2.4 L Auto) | 0.11 | 0.86 | 0.25 | 0.92 | 0.23 | 0.94 |

Chevrolet Cruze 2011 (1.8 L Manual) | 0.56 | 0.77 | 0.67 | 0.83 | 0.7 | 0.84 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 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**

Moradi, E.; Miranda-Moreno, L.
A Mixed Ensemble Learning and Time-Series Methodology for Category-Specific Vehicular Energy and Emissions Modeling. *Sustainability* **2022**, *14*, 1900.
https://doi.org/10.3390/su14031900

**AMA Style**

Moradi E, Miranda-Moreno L.
A Mixed Ensemble Learning and Time-Series Methodology for Category-Specific Vehicular Energy and Emissions Modeling. *Sustainability*. 2022; 14(3):1900.
https://doi.org/10.3390/su14031900

**Chicago/Turabian Style**

Moradi, Ehsan, and Luis Miranda-Moreno.
2022. "A Mixed Ensemble Learning and Time-Series Methodology for Category-Specific Vehicular Energy and Emissions Modeling" *Sustainability* 14, no. 3: 1900.
https://doi.org/10.3390/su14031900