Joint Modeling of Fuel Consumption and Equivalent Electricity Consumption for Plug-in Hybrid Passenger Vehicles

Abstract

To better characterize the dual-channel energy-use behavior of plug-in hybrid electric passenger vehicles (PHEVs), this study proposes a joint modeling framework for the simultaneous prediction of combined fuel economy (FC) and combined electric energy economy (EPC). Using a PHEV subset derived from the public FuelEconomy.gov database, a shared-feature gradient boosting decision tree (GBDT) framework is developed to model the fuel and electric pathways in a unified feature space. Single-task linear and tree-based models are used as baselines, and model performance is evaluated through stratified five-fold cross-validation based on vehicle category and drive type. To further reflect scenario-dependent usage patterns, the battery-electric driving share parameter, ?, is introduced to construct an equivalent energy consumption (EEC) indicator, through which scenario sensitivity and error propagation are analyzed. Results show that the proposed approach achieves strong predictive performance on both channels, with out-of-fold mean absolute errors of approximately 0.94 MPG for FC and 3.90 EMPG for EPC, and corresponding R^2values of 0.968 and 0.928, respectively. The EEC error exhibits a smooth transition from FC-dominant to EPC-dominant behavior as ?increases. Stratified analysis further reveals systematic differences in prediction accuracy across vehicle categories and drivetrain configurations. Overall, the proposed framework provides a lightweight, reproducible, and interpretable solution for joint PHEV energy-performance modeling, with potential applications in vehicle benchmarking, regulatory disclosure, and user-oriented energy-consumption assessment.

Introduction

This paper focuses on improving the evaluation and prediction of plug-in hybrid electric vehicle (PHEV) energy performance using a joint machine learning framework that simultaneously predicts fuel and electric energy economy.

Introduction

The growing shift toward low-carbon transportation has increased the importance of PHEVs, which combine an internal combustion engine with a rechargeable battery. Although they offer a balance between conventional and fully electric vehicles, accurately assessing their efficiency is challenging because their performance depends on both fuel and electricity consumption, driving behavior, battery state of charge, charging frequency, and operating conditions. Real-world studies show that PHEVs often consume significantly more fuel than official laboratory ratings due to lower-than-expected charging frequency and electric driving.

Existing research has mainly focused on:

• Energy management strategies (EMS) using optimization, reinforcement learning, and predictive control.
• Machine learning models for predicting either fuel consumption or electric energy consumption separately.

However, few studies jointly model both energy channels using publicly available datasets. This creates a gap between real-world PHEV operation and current prediction methods.

Objective

The study proposes a joint, lightweight, interpretable, and reproducible machine learning framework that:

• Simultaneously predicts combined fuel economy (MPG) and combined electric energy economy (EMPG).
• Introduces an Equivalent Energy Consumption (EEC) metric based on the battery-electric driving share (α), allowing performance evaluation under different driving scenarios ranging from fully electric to fully fuel-powered operation.
• Supports cross-vehicle benchmarking, regulatory analysis, and consumer guidance.

Data Collection and Preprocessing

The dataset was obtained from the FuelEconomy.gov database (October 2025 snapshot).

The preprocessing included:

• Selecting only PHEV passenger vehicles.
• Extracting fuel economy (comb08) and electric economy (combA08) as prediction targets.
• Removing invalid and duplicate records.
• Handling missing values using median/group imputation.
• Standardizing drivetrain, transmission, and vehicle-class information.
• Encoding categorical variables and treating outliers using IQR and Winsorization.

After filtering:

• 142 PHEV records were initially selected.
• 67 high-quality vehicle records remained for model development.
• Five-fold stratified cross-validation (by vehicle class and drivetrain) was used for evaluation.

Problem Formulation

The model treats prediction as a multi-task regression problem:

• Output 1: Combined fuel economy (MPG)
• Output 2: Combined electric economy (EMPG)

A shared feature representation is learned, followed by two independent prediction heads.

The study also defines an Equivalent Energy Consumption (EEC) indicator:

• α = 0 → fully gasoline operation
• α = 1 → fully electric operation
• Intermediate α values represent mixed driving conditions.

This enables scenario-based evaluation instead of relying on a single efficiency metric.

Analytical Framework

The proposed framework consists of:

1. Data preprocessing and feature engineering.
2. Shared multilayer perceptron (MLP) encoder.
3. Two regression heads predicting fuel and electric economy simultaneously.
4. AdamW optimization with dropout and early stopping.
5. Five-fold stratified cross-validation for reproducibility.

Evaluation

Performance is assessed using:

• Mean Absolute Error (MAE)
• Root Mean Square Error (RMSE)
• R²
• Scenario-based MAE and SMAPE across different α values
• Percentage of predictions within 10% and 20% relative error

The proposed joint model is compared against:

• Single-task learning
• Grouped models
• Non-shared architectures
• Robust loss functions
• Text-enhanced feature models

Statistical significance is evaluated using paired five-fold t-tests and confidence intervals.

Conclusion

This study proposes and validates a joint modeling approach for both fuel economy and equivalent electricity consumption. Within a unified feature space, a multi-task learning framework with shared representations is adopted, and five-fold out-of-fold evaluation is conducted on the official PHEV dataset released by the U.S. Energy Information Administration. The results show that the model achieves an overall level of accuracy that is practically useful for engineering applications across both energy-consumption channels, with out-of-fold MAE values of approximately 0.9 / 3.9 and corresponding R² values of approximately 0.97 / 0.93. The equivalent energy-consumption indicator, EMPG, exhibits clear scenario sensitivity to the battery-electric driving share, ?, and the prediction error transitions smoothly across the interval from FC-dominant to EPC-dominant behavior. Stratified analysis further reveals directional differences among different vehicle categories and drive types in terms of error structure and sensitivity. This provides empirical evidence for the subsequent introduction of conditional modeling and targeted post-processing, and indicates that, compared with simple grouped modeling or single-task modeling, the proposed joint modeling approach achieves a more appropriate balance among accuracy, stability, and interpretability. Although the model still has limitations in out-of-domain generalization and in sparsely sampled subgroups, the proposed framework has clear application potential in regulatory disclosure, product development, and user-oriented energy-consumption guidance, especially through the incorporation of additional key technical and usage features, the explicit modeling of hierarchical conditions such as vehicle category and drive type, and the introduction of uncertainty evaluation. Future work will focus on recalibration based on domestic catalog and real-world test data, as well as fusion modeling using multi-source information, including on-board operational data, road conditions, and climatic factors, in order to further improve the model’s robustness and interpretability under real driving conditions and across different climate zones. Authorship contribution: Narziev Nusratillo: Conceptualization, Methodology, Investigation, and Writing – Review & Editing. Md Borhan Uddin Niloy: Data Curation, Software, Formal Analysis, Visualization, and Writing – Review & Editing. Mohammed Shariful Islam Khan: Methodology, Validation, Resources, Investigation, and Writing – Review & Editing. Islam Shaikh Mahinur: Conceptualization, Methodology, Software, Formal Analysis, Data Curation, Visualization, Project Administration, Writing – Original Draft, and Writing – Review & Editing. All authors have read and agreed to the final version of the manuscript. Data availability: The original data used in this study are publicly available from FuelEconomy.gov. The cleaned and processed data generated during the current study, together with the modeling-related materials, are available from the corresponding author on reasonable request.

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Copyright

Copyright © 2026 Narziev Nusratillo, Md Borhan Uddin Niloy , Mohammed Shariful Islam Khan , Islam Shaikh Mahinur . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.