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Uncertainty-Aware Vehicle Energy Efficiency Prediction using an Ensemble of Neural Networks

Jihed Khiari, Cristina Olaverri-Monreal

arXiv:2304.07073v2cs.LG

TL;DR

Vehicle and operating-condition variability makes energy-efficiency prediction uncertain, and manufacturer estimates may differ from real-world use. The paper uses an ensemble of neural networks to predict efficiency and quantify uncertainty. Its ensemble performs significantly better than baselines for fuel-efficiency tasks across ICE, PHEV, and HEV vehicles, while battery-efficiency gains are not always significant.

  • Problem

    Vehicle-use conditions vary, and manufacturer efficiency knowledge can diverge from real-world use, complicating energy-efficiency prediction.

    Source: §I · p. 1

  • Method

    An ensemble of neural networks predicts vehicle energy efficiency and outputs a measure of prediction confidence.

    Source: §I · p. 1

  • Results

    Fuel-efficiency predictions significantly outperform baselines for ICE, PHEV, and HEV vehicles, while battery-efficiency gains are mostly not significant, including for EV and HEV.

    Source: C. Results · p. 6

  • Takeaways & Limitations

    The ensemble provides accurate predictions and confidence information across vehicle types and energy types in the evaluated VED setting.

    Source: §V · p. 7, §VI · p. 7

    Neural-network ensembles require more initial training time than decision-tree-based ensembles, although test-time predictions are fast.

    Source: §V · p. 7

Abstract

from arXiv · show

The transportation sector accounts for about 25% of global greenhouse gas emissions. Therefore, an improvement of energy efficiency in the traffic sector is crucial to reducing the carbon footprint. Efficiency is typically measured in terms of energy use per traveled distance, e.g. liters of fuel per kilometer. Leading factors that impact the energy efficiency are the type of vehicle, environment, driver behavior, and weather conditions. These varying factors introduce uncertainty in estimating the vehicles' energy efficiency. We propose in this paper an ensemble learning approach based on deep neural networks (ENN) that is designed to reduce the predictive uncertainty and to output measures of such uncertainty. We evaluated it using the publicly available Vehicle Energy Dataset (VED) and compared it with several baselines per vehicle and energy type. The results showed a high predictive performance and they allowed to output a measure of predictive uncertainty.

I. INTRODUCTION

Vehicle energy efficiency varies with vehicle and operating conditions, making real-world prediction challenging. The paper proposes an uncertainty-aware neural-network ensemble and evaluates it across vehicle and energy types.

I. INTRODUCTION

  • Energy efficiency relates energy use to work achieved, such as moving a distance or carrying a load, unlike total energy consumption alone.The introduction notes that two vehicles can use the same energy yet differ in how efficiently they convert it into motion.Source: §I · p. 1
  • Vehicle type, size, fuel or electric energy use, temperature, and road type can affect energy use.The paper frames these varying circumstances as relevant to estimating efficiency.Source: §I · p. 1
  • Manufacturer information may diverge from real-world use; one cited report found a 10% gap between official and on-road fuel consumption rates for new cars.The authors motivate estimates based on ground-truth data reflecting vehicle use, environment, weather, and driver behavior.Source: §I · p. 1
  • The proposed ensemble of neural networks predicts energy efficiency and provides a measure of confidence in its predictions.The authors also investigate the ensemble, its base learners, and scoring functions.Source: §I · p. 1
  • The evaluation uses the publicly available VED, which spans over a year and includes trips by several vehicle types.The paper presents evaluation per vehicle and energy type and compares the approach with several baselines.Source: §I · pp. 1–2
  • The approach does not require complex physical, chemical, or kinetic models or manufacturer efficiency measures, and is not limited to one vehicle type.The authors describe it as adaptable to the dataset at hand.Source: §I · p. 1

II. RELATED WORK

Prior efficiency-estimation work includes physical, data-driven, and hybrid approaches, while many methods rely on manufacturer data or focus on one vehicle type. This paper studies uncertainty-aware neural-network ensembles for efficiency prediction across vehicle types.

II. RELATED WORK

  • Many available works rely on manufacturer estimates or complex physical, kinetic, or chemical models, and typically focus on one vehicle type.The paper proposes prediction across vehicle types based solely on floating-car data containing instantaneous energy consumption or measures for estimating it.Source: §II · p. 2
  • Trip-efficiency estimation approaches use mechanical, dynamic, or kinetic data; data-driven energy data; or combinations of these approaches.The cited examples include vehicle-specific power models and hybrid statistical and load-based modeling,,,,,,,.Source: §II · p. 2
  • Deep neural networks can produce incorrect high-confidence outputs, while Bayesian networks for uncertainty quantification can be complex and computationally expensive.The related work notes simpler DNN ensembles as a potentially useful, deployable uncertainty-quantification approach.Source: §II · p. 2
  • The authors identify a gap: to their knowledge, uncertainty-aware ensemble prediction had not been used for energy-efficiency prediction across different vehicle types.They study the usability of such an ensemble for uncertainty-aware predictions in this setting.Source: §II · p. 2

III. METHODOLOGY

The study processes vehicle and energy data into trip-level efficiency predictions, using the Vehicle Energy Dataset (VED), which combines dynamic driving records with static vehicle information. The fleet contains 383 personal cars classified by energy source.

A. Problem Formulation

  • The workflow divides vehicle data by vehicle type, generates relevant features, computes trip-level energy efficiency, and trains an ensemble to predict test-trip efficiency.Figure 2b summarizes the process.Source: A. Problem Formulation · p. 2

B. Data Description

  • VED dynamic data were collected at one-second granularity from November 2017 to November 2018, without driver-identifying information.Source: B. Data Description · pp. 2–3
  • The 383-car fleet comprises 264 ICE, 92 HEV, and 27 PHEV or EV vehicles, classified by energy source.VED combines dynamic and static data to identify trips and vehicles; its dynamic records include GPS trajectories and time series for fuel, energy, speed, and auxiliary power.Source: B. Data Description · pp. 2–3
  • Trips span different times of day, seasons, and road types, although road type is not a dataset attribute; most trips last under 10 minutes.ICE trip counts are considerably higher than those of other vehicle types.Source: B. Data Description · p. 3

C. Data Preprocessing

The preprocessing stage estimates energy consumption, then expresses efficiency as distance traveled per unit of energy. It uses separate efficiency units for fuel and battery energy.

1) Energy efficiency estimation:

2) Feature Engineering:

Feature engineering adds temporal and trip-level speed descriptors and clusters trips by origin and destination. The resulting cluster number is included as a dataset feature.

2) Feature Engineering:

  • Timestamp-derived hour, minute, month, and day-of-week features, plus descriptive statistics about trip speed, augment the existing data.Source: 2) Feature Engineering · p. 3
  • Origin-destination clustering groups trips by shared geography or patterns, and the resulting cluster number becomes a feature.Cluster 2 represents trips with concentrated start and end areas, while Clusters 6 and 7 span larger geographical areas.Source: 2) Feature Engineering · pp. 3–4
  • The fuel-consumption algorithm uses FuelRate when available, otherwise falls back to MAF, then to an AbsLoad-and-RPM branch.Source: 2) Feature Engineering · p. 4

D. Ensemple Approach

The ensemble models probabilistic predictions with deep neural networks and combines independently trained networks as a uniformly weighted mixture. Training uses stratified data batches that represent all months of the year.

D. Ensemple Approach

  • Stratified training batches consider all months of the year; after random batch sampling, chronological order is restored.Source: D. Ensemple Approach · pp. 4–5
  • Each neural network models a probabilistic predictive distribution and outputs predicted mean and variance, trained by minimizing Gaussian negative log-likelihood.The method identifies three aspects: a scoring rule to reduce predictive uncertainty, adversarial training to smooth predictive distributions, and an ensemble of M neural networks.Source: D. Ensemple Approach · p. 4
  • Networks are trained independently in parallel using random data batches and random parameter initializations.Source: D. Ensemple Approach · p. 5
  • The ensemble combines network predictions as a uniformly weighted mixture model.Source: D. Ensemple Approach · p. 5

IV. EXPERIMENTS AND RESULTS

The experiments compare the neural-network ensemble with regression and tree-based baselines, using a stratified train/test split and regression metrics.

A. Experimental Setup

  • The split yields balanced training and test sets chronologically, with both sets containing proportionate samples from all months, unlike a sequential split that can leave months unrepresented across sets.Source: A. Experimental Setup · p. 5
  • The ensemble is compared with linear regression, random forest, XGBoost, and a single neural network.The single neural network uses the same settings and parameters as the ensemble’s individual models.Source: A. Experimental Setup · p. 5
  • Performance is evaluated using RMSE on the same test set and the R2 score.The paper describes R2 as the proportion of dependent-variable variance predictable from the independent variables.Source: A. Experimental Setup · p. 6

B. Statistical Analysis

The authors use a one-tailed Wilcoxon signed-rank test to compare ensemble errors with each baseline, without assuming normally distributed errors.

B. Statistical Analysis

  • The Wilcoxon signed-rank test compares paired model errors by ranking the magnitudes of their differences, without assuming normality.Its null hypothesis is that the median difference between paired samples is zero.Source: B. Statistical Analysis · p. 6
  • The test statistic is the smaller of the rank sums for positive and negative paired differences.Source: B. Statistical Analysis · p. 6
  • The one-tailed test asks whether the first model has smaller error than the second, with significance level 0.05.The ensemble is tested against each baseline.Source: B. Statistical Analysis · p. 6

C. Results

The results report predictions and uncertainty across vehicle and energy types, with performance compared by RMSE and R2 and significance assessed against baselines.

C. Results

  • Figure 5 plots mean predictions as lines and predictive uncertainty as lighter shaded ranges, with wider ranges indicating greater uncertainty.Fuel predictions are in Km/L and battery predictions in Km/kWh; HEV battery results cover only July through October because of limited data.Source: C. Results · p. 6
  • Test results are reported by month because the stratified split includes samples from every month in both sets.Source: C. Results · p. 6
  • The ensemble’s R2 scores range from 0.74 to 0.92 across six vehicle-and-energy prediction tasks.XGBoost has higher R2 for PHEV and EV battery-efficiency prediction.Source: C. Results · p. 6
  • For fuel-efficiency prediction, the ensemble significantly outperforms the other baselines across ICE, PHEV, and HEV; battery-task gains are less consistently significant.For PHEV battery efficiency, it significantly outperforms LR, RF, and XGB, but not NN; for EV and HEV battery tasks, it significantly outperforms none.Source: C. Results · p. 6

V. DISCUSSION

The discussion presents the ensemble as accurate across vehicle and energy types while using uncertainty ranges to communicate prediction confidence amid variable data.

V. DISCUSSION

  • Fuel-efficiency predictions for ICE and HEV have higher means and narrower uncertainty ranges than PHEV predictions, whose fluctuations indicate lower confidence.Source: §V · p. 6
  • Uncertainty ranges increase in colder months and from July to August for battery-equipped vehicles; the authors suggest weather and air-conditioning use as possible explanations.The year-long data include 383 vehicles and implicitly capture variation in drivers and driving conditions, although driver identities are unavailable.Source: §V · pp. 6–7
  • The proposed ensemble approach predicts energy efficiency accurately according to RMSE and R2 scores; statistical testing found significantly higher performance than baselines in most cases, with consistent performance across vehicle and energy types.Source: §V · p. 7
  • ENN has the lowest RMSE in all cases except HEV and EV battery efficiency, where XGBoost performs better; its RMSE standard deviations are consistently smaller than the baselines’.The authors relate XGBoost’s advantage in those battery tasks to the smaller training data available, and note that DNNs require substantial data for sufficient training.Source: §V · p. 7, Table IV · p. 7
  • The authors report significantly higher performance than baselines in most cases and describe the approach as versatile across vehicle and energy types.The Wilcoxon results are summarized in Table VI.Source: §V · p. 7, Table VI · p. 7
  • The ensemble requires more initial training time than decision-tree ensembles, but can provide fast test-time predictions.The authors also report consistent training and test performance and deem the year-long data sufficient.Source: §V · p. 7
  • Using floating-car and sensor data, the approach is proposed for fleet management and trip planning where uncertainty information can inform decisions, trust, and energy-saving policies.Source: §V · p. 7

VI. CONCLUSION

The ENN was evaluated on the publicly available VED, which covers different vehicle types over a year, and the authors report high predictive accuracy alongside information about model confidence. They identify future work on uncertainty measures and separating aleatoric from epistemic uncertainty.

VI. CONCLUSION

  • The VED-based ENN achieved high predictive accuracy while also providing information about the model’s confidence in its output.The dataset includes different vehicle types over a period of a year.Source: §VI · p. 7
  • Predictions are presented per vehicle, energy type, and month, with fuel-related values in blue solid lines and electric-based values in red dashed lines.Figure 5 shows the ensemble predictions.Source: Figure 5 · p. 8
  • Confidence information is described as facilitating decision making and increasing trust in the model’s output.The conclusion links this benefit to information about model confidence.Source: §VI · p. 8
  • Future work will investigate other uncertainty measures and uncouple aleatoric and epistemic uncertainty in this context.Source: §VI · p. 8

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