Development and Evaluation of Velocity Predictive Optimal Energy Management Strategies in Intelligent and Connected Hybrid Electric Vehicles

Abstract

In this study, a thorough and definitive evaluation of Predictive Optimal Energy Management Strategy (POEMS) applications in connected vehicles using 10 to 20 s predicted velocity is conducted for a Hybrid Electric Vehicle (HEV). The presented methodology includes synchronous datasets gathered in Fort Collins, Colorado using a test vehicle equipped with sensors to measure ego vehicle position and motion and that of surrounding objects as well as receive Infrastructure to Vehicle (I2V) information. These datasets are utilized to compare the effect of different signal categories on prediction fidelity for different prediction horizons within a POEMS framework. Multiple artificial intelligence (AI) and machine learning (ML) algorithms use the collected data to output future vehicle velocity prediction models. The effects of different combinations of signals and different models on prediction fidelity in various prediction windows are explored. All of these combinations are ultimately addressed where the rubber meets the road: fuel economy (FE) enabled from POEMS. FE optimization is performed using Model Predictive Control (MPC) with a Dynamic Programming (DP) optimizer. FE improvements from MPC control at various prediction time horizons are compared to that of full-cycle DP. All FE results are determined using high-fidelity simulations of an Autonomie 2010 Toyota Prius model. The full-cycle DP POEMS provides the theoretical upper limit on fuel economy (FE) improvement achievable with POEMS but is not currently practical for real-world implementation. Perfect prediction MPC (PP-MPC) represents the upper limit of FE improvement practically achievable with POEMS. Real-Prediction MPC (RP-MPC) can provide nearly equivalent FE improvement when used with high-fidelity predictions. Constant-Velocity MPC (CV-MPC) uses a constant speed prediction and serves as a “null” POEMS. Results showed that RP-MPC, enabled by high-fidelity ego future speed prediction, led to significant FE improvement over baseline nearly matching that of PP-MPC.

1. Introduction

Improving FE is a critical goal to reducing climate change and air pollution. The transportation sector is responsible for 27% of all greenhouse gas emissions produced globally and more than 50% of nitrogen oxide emissions [1]. Recent studies show that greenhouse gas emissions are a significant contributor to global climate change [2] and lowered life expectancy in many countries [3]. Greenhouse gas emission levels are directly related to the FE of vehicles; reducing total miles driven is a difficult-to-implement and politically controversial goal, thus much research into methods to improve vehicle fuel economy (FE) has been performed [4].

A critical component of improving FE is vehicle electrification. Recently, Hybrid Electric Vehicles (HEV) and Plug-in Hybrid Electric Vehicles (PHEV) have been widely researched because of their greater potential to increase fuel economy (FE) and emissions over that of conventional Internal Combustion Engine (ICE) vehicles [5]. However, currently available HEVs do not operate optimally [6].

In addition to advancements in powertrain technology, recent developments in the automotive industry have led to huge advancements in Intelligent and Connected Vehicle (ICV) technology. Advanced Driver Assistance System (ADAS) technology has seen rapid market penetration due to its potential to bring safety and convenience benefits to customers [7,8,9]. Automation (i.e., ADAS) and connectivity (i.e., ICV) technology are critical technologies not only for safety and commercialization of autonomous vehicles but also for energy efficiency through implementation of Predictive Optimal Energy Management Strategies (POEMSs) on HEVs and PHEVs which can increase their FE and reduce their emissions [10,11,12,13,14].

POEMSs use predicted vehicle velocity (enabled through ADAS [15] and connectivity) as an input to optimal control. The optimal solution output is then used as an input to the vehicle plant, ideally an HEV or PHEV due to the additional operational degrees of freedom [16]. This process has been the subject of active research since the first publication in 2001 [10]. Note that in the current transportation environment, perfect future velocity prediction is not possible. To address this issue, researchers have used Model Predictive Control (MPC) which, in this context, is the application of DP optimization to fixed length prediction windows. Research in this space has demonstrated that perfect velocity prediction is not required [17], and that even heuristic approaches which rely on acceleration event prediction can be used [12,18] to achieve improvements in FE. However, it is worth noting that these FE improvements are modest compared to those theoretically achievable with prefect prediction of vehicle velocity. High-fidelity prediction of future vehicle velocity is presently achievable through the employment of machine learning (ML) and Artificial Neural Network (ANN) methods and ICV technology [19,20,21,22,23,24,25,26]. Despite all of this research, a thorough investigation of the datasets and prediction models’ effect on vehicle FE (the full system) has not been conducted. The latest research has explored the effect on velocity prediction error metrics rather than resultant vehicle FE [26,27]. In order to facilitate real-world implementation, certain specific research gaps must be addressed; these research gaps are defined in [16] as:

• Performance of Optimal EMS with Actual Velocity Predictions;
• Performance of Optimal EMS when Subjected to Disturbances;
• Performance of Optimal EMS in Real Vehicles.

To the author’s knowledge, this paper represents the first comprehensive study fully addressing Research Gap 1. Previous research in the area of POEMS has focused on select aspects of Research Gap 1 but no comprehensive study has been performed which concerns the use of real-world data and real-time prediction methods in POEMS. This study, being such a comprehensive analysis, allows for research to progress towards other aspects of implementation namely Research Gaps 2 and 3. Previous research in this area is summarized as follows. The efficacy of predictive Optimal EMS for improving efficiency in HEVs was first shown in 2001 in [10] utilizing perfect prediction. In 2008, velocity prediction was introduced to the literature in [28] which used an analytical traffic based velocity prediction model. In 2015, the advantages of ANN prediction were shown in [21,22]. In 2017 and 2018, a series of studies [15,17,29,30] experimented with different data streams to optimize prediction with a shallow ANN. In 2019, more modern machine learning techniques were introduced into the field in [31] where reinforcement learning was used along with traffic data to train an ANN to produce optimal controls for a power-split hybrid. Also in 2019, Refs. [26,32] showed that high-fidelity predictions were possible through the use of deep Long Short-Term-Memory (LSTM) ANNs. Finally, in 2020, a thorough analysis of various combinations of real-world data streams and machine learning techniques [26,27,33] showed that the highest degree of prediction fidelity could be attained through the use of LSTM ANNs with the use of signal phase and timing (SPaT) and lead vehicle data.

Thus, in order to close the gap, this paper outlines a comprehensive system-level study addressing the interactions between groups of available real-world data, velocity prediction methods, and Optimal EMS methods with respect to the overall system output: FE.

This paper rigorously evaluates the dataset and perception model for POEMS and evaluates performance using the FE for a validated HEV to enable full system performance insight, which to-date is missing from the literature. Cutting-edge AI technology is leveraged to generate high-fidelity future vehicle velocity predictions in 10 to 20 s windows. The predictions are fed into an MPC control method in order to determine the optimal instantaneous torque split for a power-split HEV. The FE achievable with the proposed POEMS will be compared to that achievable with perfect prediction full-drive-cycle DP (FCDP), perfect prediction MPC (PP-MPC), constant velocity-prediction MPC (CV-MPC), and Autonomie baseline control. This paper will further show that the proposed method is implementable on current vehicles with current technology and has the potential to provide significant FE improvements within the HEV fleet if implemented.

2. POEMS Methodology

2.1. Overall System

HEV POEMS uses predictions of future vehicle velocity to inform an optimal powertrain control strategy, thus achieving greater energy efficiency. Powertrain controls include torque split and gear shifting based on powertrain states such as battery State of Charge (SOC) and current gear in the case of a parallel power-train configuration or only torque split in the case of a parawhnllel configuration.

As shown in Figure 1, a POEMS consists of three major subsystems. The first is the perception system which predicts vehicle motion using information about previous and current vehicle motion, powertrain states, driver inputs, eh ADAS, and V2X data as inputs. The second is the planning subsystem which computes optimal controls based on the predicted vehicle velocity. Finally, the third subsystem is the vehicle plant which can be either the physical vehicle or high-fidelity simulation model of the vehicle. The final system outputs are the actual vehicle velocity and powertrain states.

POEMS achieve greater FE by ensuring that the engine is used in regions of maximum efficiency as often as possible. This concept is shown in Figure 2 which includes a Brake-Specific Fuel Consumption (BSFC) map for an example engine and different combinations of engine speed and torque which produce different engine efficiencies. Thus, most engine controllers attempt to operate the engine along its Ideal Operating Line (IOL) [34] which contains the most efficient torque for a given engine speed. POEMS use information about future vehicle velocity to ensure that the engine only operates in the most efficient segment of the IOL, what can be thought of as an Ideal Operating Line Segment (IOLS).

As shown in Figure 2, simply operating along the IOL (yellow dots) does not guarantee efficient operation. POEMSs increase FE by guaranteeing operation within the IOLS (green dots).

Although this paper only concerns vehicle motion, the POEMS method can be extended to account for additional exogenous inputs such as cabin heating and cooling requirements [35,36,37] without fundamentally changing the method.

2.2. System Inputs

2.2.1. Dataset Development

The first step in the development of practical and high-fidelity real-world future vehicle speed prediction was to collect a sample generic dataset which would represent all data sources potentially available to a given ICV. All data sources selected are currently available to ICVs or will be available in the near future [38]. In this section, a taxonomy for such a dataset is defined. This taxonomy defines data both in terms of source form and processed form and defines the process of transformation.eh

The first step in defining the dataset is to define the sources of the data. Three distinct source categories are proposed:

• VEH: Vehicle operational data such as vehicle motion, performance, and driver inputs. These data only concern the ego vehicle itself and its driver.
• ADAS: Advanced Driver Assistance System (ADAS) data [39]. This consists of the data generated by external object sensors on the vehicle and concerns objects within the vehicle’s line of sight.
• V2I: Data which the vehicle receives through connectivity to infrastructure and other vehicles.

In order to be considered an ICV, a vehicle must receive information from all three of the above sources. Most modern vehicles receive data from the VEH and ADAS sources [40] and V2I is available in some regions [41]. These signals were obtained from the ego vehicle CAN bus and the City of Fort Collins, Colorado.

Within these source categories, signals of use in vehicle future velocity prediction are shown in

Table 1. Data sources and associated signals.

Data Source	Signal	Description
VEH	General Vehicle Signals	Signals such as speed, acceleration, throttle position, and steered angle which can be found via CAN on any vehicle
VEH	Historical Speeds (HS)	Historical speed data for the vehicle at the current location
ADAS	Lead Vehicle Track (LV)	Relative location of confirmed lead vehicle from ADAS system
V2I	Signal Phase and Timing (SPaT)	Signal phase and timing of next traffic signal
V2I	Segment Speed (SS)	Traffic speed through current road segment

.

All VEH signals should be available on all modern vehicle CAN networks while ADAS-enabled vehicles will produce a lead vehicle track for safety and Autonomous Cruise Control (ACC) purposes. The information for SPaT and SS comes form the SAE J2735 SPaT/Map message. Thus, all signals used in this study are available to a generic ICV while traveling on a connected infrastructure. Most modern vehicles will have access to the VEH and ADAS sourced signals. A total of 13 drive cycles worth of data were collected along the data drive cycle by one driver over two days. Details about data collection and availability can be found in the team’s previous work [33].

2.2.2. Data Drive Cycle Selection

In order to gauge the effects of real-world data-based predictions on the performance of POEMS, a real-world dataset was required. It was desired to gather data in conditions which would allow for optimal POEMS performance such that the relative differences between various POEMS methods would be as great as possible. A secondary consideration was that, in order to allow for optimal ML and ANN prediction performance, the data collection should be conducted along a repeating drive cycle and that this cycle should be short enough that more than 10 cycles could be collected in a single day. The drive cycle which was selected was a 4 mile long drive cycle along urban arterial roads in downtown Fort Collins, Colorado which is shown in Figure 3.

In order to assess the characteristics of the data drive cycle, it was determined that the data drive cycle and the EPA dynamometer drive cycles should be characterized by their distributions of speeds and accelerations. These basic statistical measures were chosen in order to allow for easy comparison between the drive cycles. The drive cycle characteristics data are shown in

Table 2. Drive cycle characteristics for data drive cycle and EPA drive cycles.

Drive Cycle	Mean Non-Zero Speed (MNZS)	Standard Deviation of Non-Zero Speeds (SNZS)	Mean Absolute Acceleration (MAA)	Standard Deviation of Absolute Accelerations (SAA)
Data	18.6988	8.5699	1.1557	1.1432
UDDS	10.7923	5.5850	0.4723	0.4859
US06	23.1791	9.5014	0.6538	0.7851
HWFET	21.7191	4.1752	0.1713	0.2443

.

Based on these characteristics, the similarity of the data drive cycle and the EPA dynamometer drive cycles was calculated using the multivariate normal distribution. The relative similarities between the EPA cycles and the data drive cycle are shown in

Table 3. Relative similarities between EPA dynamometer drive cycles and the data drive cycle.

UDDS	US06	HWFET
0.5885	0.2394	0.1721

.

It must be stressed that the comparison between a data drive cycle and the EPA dynamometer drive cycles could only be calculated after data collection was performed and the data drive cycle was known. Of the candidate data drive cycles tried, the drive cycle shown in Figure 3 resulted in the most favorable comparison to EPA dynamometer drive cycles.

The selected data drive cycle was most similar to the UDDS EPA dynamometer drive cycle because higher numbers imply that the real-world drive cycle from Figure 3 is more similar.

2.3. Subsystem 1: Perception

Having collected an extensive real-world ICV dataset, a comprehensive study on prediction methods was conducted. The initial analysis of the prediction study can be found in [26] and is summarized below:

A wide field of potential prediction algorithms including classical ML and ANN methods were considered. The candidate methods are listed in

Table 4. Candidate Prediction Methods.

Method	Method Type
Long Short Term Memory (LSTM) Deep Neural Network (DNN)	ANN
Convolutional Neural Network (CNN)	ANN
CNN-LSTM	ANN
Decision Trees	ML
Bagged Trees	ML
Random Forest	ML
Extra Trees	ML
Ridge	ML
K-Nearest-Neighbors (KNN)	ML
Linear Regression without Interactions (LR)	Statistical
Linear Regression with Interactions (LRI)	Statistical

.

All methods were trained, tested, and validated on a 9/2/2 data-split basis, respectively. The training and evaluation metric was Mean Absolute Error ($MAE$), where X is the predicted velocity value, Y is the actual velocity value, and n is the total number of timesteps.

$$MAE(X,Y)=\frac{{\sum }_{i=1}^n|X_i-Y_i|}{n}$$

(1)

An extensive study was conducted on different combinations of the signals in Table 1 as well as different combinations of macro-parameters for the methods. From this general study, the best results for each method for 10, 15, and 30 s time horizon speed predictions in terms of $MAE$ are listed in

Table 5. The candidate prediction methods results organized from best performing to worst performing.

Method	MAE—10 s	MAE—15 s	MAE—20 s
LSTM	1.78	2.55	3.09
CNN	1.84	2.77	3.50
CNN-LSTM	1.97	2.7	3.26
Decision Trees	2.69	3.60	4.12
Bagged Trees	2.23	3.09	3.67
Random Forest	2.30	3.15	3.72
Extra Trees	1.99	2.73	3.30
Ridge	2.67	3.84	4.67
KNN	2.67	3.84	4.67
LR	2.65	3.82	4.65
LRI	2.57	3.60	4.28

.

The results of the general study showed that the LSTM had the best performance at 10, 15, and 20 s.

Based on this collected evidence, it was concluded that an LSTM should be used within the POEMS system. For further discussions and details, the reader is referred to the team’s previous publications [26,27].

2.4. Subsystem 2: Planning

HEV POEMS planning subsystems generally fall into two groups: (1) those based on Pontryagin’s Maximum Principle (PMP) such as ECMS [42], a-ECMS [11], as well as their derivatives, and (2) those based on DP. The advantages of PMP methods is that these are “real-time” strategies since they are relatively computationally cheap. However, this method is typically non-optimal and recent research suggests that the equivalence factor prediction is analogous to velocity prediction [43]. The advantages of DP based methods is that they guarantee discovery of the globally optimal solutions assuming that the vehicle velocity prediction is accurate. The research team discovered the critical importance of this aspect through documenting that even if significant and real-world velocity mispredictions are present, the solution is still near optimal [44] which has lead to new method of real-world practical implementation [12,18]. Additionally, the rise in the use of AI within the CAV space has led to deployments of vehicles with high-performance GPUs on-board the vehicle which potentially enables real-time computation of DP [45], which has been a common criticism for eventual DP implementation. For these reasons, DP methods were selected for this study.

DP is a numerical method based on Bellman’s principle of Optimality, which solves multistage decision-making problems and finds the global optimal solution by operating recursively backwards through time and storing only the optimal controls at each step [46,47]. DP and its derivative strategies have been applied to the problem of FE optimization for HEVs previously [6,10,48,49] for full and partial drive cycles as well as for perfect and real predictions.

DP can be thought of as a recursive equation solver with memory. A recursive solution to a problem is to evaluate all possible paths by evaluating every possible combination of decisions independently. While a recursive solution will find a global optimum, it will require an exponentially increasing number of function evaluations for each additional time-step. DP solves this run-time problem by iterating backwards through time and storing the optimal controls for each discreet state value at each time-step then evaluating the same controls from the same discreet state values until the first time-step. The result of the backward iteration is an optimal control matrix which can be used to find optimal controls at each time-step based on the current state values when iterating forwards. The backwards iteration step is referred to as the optimization step while the forward iteration step is referred to as the evaluation step. The DP method is shown schematically in Figure 4.

The optimization step of the DP method, as shown in Figure 4, creates an optimal matrix which can be used to compute optimal controls at each step by combining current and “remembered” costs. The optimization step iterates backwards from the last time-step (N) to the first which is not shown. The state values (represented by solid-outlined circles) show discreet state values. At time-step N-1, the model is evaluated for each of the discreet state values at each discreet control value which results in a series of new “intermediate” state values (represented by dashed-outlined circles) and associated control costs. Following this, the lowest cost (optimal) control is selected for each discreet state value. At time-step N-2 the same process is repeated but in addition to the control cost, the cost-to-go is calculated and added. The cost-to-go from a given intermediate state value is calculated by interpolating from the stored optimal control costs from state N-1. This process repeats itself until the first time-step is reached. The DP method shown in Figure 4 is constrained in two ways: (1) a large penalty is applied for distance from the desired end state value at time-step N which forces the optimal controls for all state values at time-step N-1 to produce the same state value at time-step N and (2) controls which lead to intermediate states which are above or below the maximum and minimum value lines (represented by red dashed-outlined circles), respectively, are not considered. The output of the optimization step is an optimal control matrix which stores the optimal controls for each discreet starting state value at each time-step.

The evaluation step of the DP method, also shown in Figure 4, iterates forward from the first time-step through the last time-step from a given starting state value. At each time-step, interpolation is performed using the starting state value (represented by blue solid-outlined circles) and the optimal control matrix values for the current time-step to determine the optimal control for the current time-step. The optimal control is then applied and the starting state value for the subsequent time-step is calculated. This process is repeated until the penultimate time-step is reached.

2.4.1. High-Fidelity DP Solution for the HEV Optimization Problem

The formulation of the DP problem for the 2010 Toyota Prius is as follows:

• The powertrain state x is the battery $SOC$;
• The powertrain control u is the engine power;
• The exogenous input for the powertrain w is the vehicle speed;
• The time index k denotes the current time-step.

The general form of the dynamic equation is shown below. It uses a high-fidelity model of the vehicle to generate the $SOC$ at time-step $k+1$ based on the $SOC$ at time-step k, the engine power at time-step k, and the vehicle speed at time-step k as:

$$x(k+1)=x\left(k\right)+f\left(x\right(k),u(k),w(k\left)\right)\Delta \left(t\right)$$

(2)

where $f\left(x\right(k),u(k),w(k\left)\right)$ is the charging/discharging rate for the battery $dSOC/dt$. The charging/discharging rate function $f\left(x\right(k),u(k),w(k\left)\right)$ can be written out as:

$$\frac{dSOC}{dt}=\frac{P_{batt}{ϵ}_{chg}}{V_{oc}C}=\frac{(P_{batt,mot}+P_{batt,gen}){ϵ}_{chg}}{V_{oc}C}$$

(3)

where $V_{oc}$ and C are the battery open-circuit voltage and charge capacity, respectively. The charging/discharging efficiency is defined as:

$${ϵ}_{chg}=\left\{\begin{array}{cc}{C}_{chg}\hfill & P_{batt}\ge 0\hfill \\ C_{dchg}\hfill & P_{batt}<0\hfill \end{array}\right.$$

(4)

where $C_{chg}$ and $C_{dchg}$ are constants reflecting the battery’s efficiency in charging and discharging, respectively. The powers $P_{batt,mot}$ and $P_{batt,gen}$ are calculated as follows:

$$\begin{array}{c}{P}_{batt,mot}=\frac{T_{mot}{\omega }_{mot}}{{ϵ}_{mot}}\end{array}$$

(5)

$$\begin{array}{c}{P}_{batt,gen}=\frac{T_{gen}{\omega }_{gen}}{{ϵ}_{gen}}\end{array}$$

(6)

The efficiencies ${ϵ}_{mot}$ and ${ϵ}_{gen}$ are the efficiencies of the motor and generator, respectively. Note that the efficiencies are in the denominator as the terms $P_{batt,mot}$ and $P_{batt,gen}$ are the power that the battery must provide to each to produce the required output powers $P_{mot}=T_{mot}{\omega }_{mot}$ and $P_{gen}=T_{gen}{\omega }_{gen}$ The following process is followed:

Starting with the current vehicle speed $w\left(k\right)$ and acceleration $\dot{w}\left(k\right)$ the vehicle power can be calculated using the road loads power equation.

$$P_{veh}=(m\dot{w}\left(k\right)+A+Bw\left(k\right)+Cw{\left(k\right)}^2)w\left(k\right)$$

(7)

where m is the vehicle mass and A, B, and C are vehicle-specific constants. For a given engine power $u_i$, the electric power required is:

$$P_{elec}=P_{veh}-u_i$$

(8)

For the given $u_i$, the engine torque and speed can be interpolated from the engine IOL and the combination of engine speed (${\omega }_{eng}$) and torque ($T_{eng}$) along with electric power can be used to determine the torques and speeds of the motor and generator from the planetary gearset dimensions.

The torques are calculated as follows:

$$\begin{array}{c}{T}_{whl}=\frac{P_{veh}{R}_{whl}}{w\left(k\right)}\end{array}$$

(9)

$$\begin{array}{c}{T}_{pt}=\frac{T_{whl}}{{\rho }_{fd}}\end{array}$$

(10)

$$\begin{array}{c}{T}_{gen}=\frac{-\rho }{1+\rho }{T}_{eng}\end{array}$$

(11)

$$\begin{array}{c}{T}_{ring}=-\rho (T_{gen}-T_{eng})\end{array}$$

(12)

$$\begin{array}{c}{T}_{mot}=T_{pt}-T_{ring}\end{array}$$

(13)

where $T_{whl}$ and $R_{whl}$ are the torque applied at and the radius of the driven wheels, respectively, $T_{pt}$ is the output torque of the power-train (before the differential) and ${\rho }_{fd}$ is the final drive ratio, $\rho$ is the gear ratio of the sun gear to the ring gear for the planetary gearset, $T_{ring}$ is the torque of the ring gear, $T_{gen}$ is the torque of the generator, $T_{eng}$ is the torque of the engine, and $T_{mot}$ is the torque of the motor.

And the speeds are calculated as follows:

$$\begin{array}{c}{\omega }_{whl}=\frac{w\left(k\right)}{R_{whl}}\end{array}$$

(14)

$$\begin{array}{c}{\omega }_{mot}={\omega }_{ring}={\rho }_{fd}{\omega }_{whl}\end{array}$$

(15)

$$\begin{array}{c}{\omega }_{gen}=\frac{\rho +1}{\rho }{\omega }_{eng}-\frac{{\omega }_{ring}}{\rho }\end{array}$$

(16)

where $R_{whl}$, $R_{sun}$, and $R_{ring}$ are the radii of the wheel, sun gear, and ring gear, respectively, $T_{pt}$ is the torque produced by the powertrain before the differential, and ${\rho }_{fd}$ is the final drive ratio.

The cost function for the DP problem for control $u_i$ at time-step k can be formulated as either a FE maximization or a fuel consumption minimization. Since fuel consumption minimization is more intuitive and widely used in previous studies, it will be utilized in this study.

$$J_i\left(k\right)=J_{im}+\left\{\begin{array}{cc}{J}_{ctg}\hfill & k>N\hfill \\ J_{pen}={(x_f-x(k+1))}^2{C}_{pen}\hfill & k=N\hfill \end{array}\right.$$

(17)

where $J_{im,i}$ is the cost of fuel consumed to reach the intermediate state value which is calculated using the engine speed and torque and the engine FC map, $J_{ctg}$ is the cost-to-go to the next state which is calculated through integration, and $J_{pen}$ is the manually assigned penalty function associated with not arriving at the desired final $SOC$ at the final time-step $k=N$.

2.4.2. Model Predictive Control (MPC) Methods

MPC is a framework to implement prediction-based optimal control. It utilizes a model of the system and a fixed time horizon to generate operational decisions. The DP model discussed in the previous section can be directly utilized in a fixed-horizon MPC framework with a few modifications.

The FCDP and a generic MPC methods are shown schematically in Figure 5.

In effect, MPC performs the DP method on a shortened drive cycle at each step of the actual drive cycle. Naturally, MPC should take significantly longer to run on a per time-step basis as full drive cycle DP. A more detailed explanation can be found in [26].

2.5. Subsystem 3: Vehicle Plant

This study was conducted using a validated Autonomie model of a 2010 Toyota Prius. The 2010 Prius is equipped with a Toyota e-CVT gearbox which utilizes two electric motors (motor and generator) connected to the engine and the differential through a planetary gearset to create a Continuously Variable Transmission (CVT) [50]. Because of the e-CVT architecture, the Prius driveline is controlled entirely by torque commands without having distinct gear states, thus the only powertrain control for the Prius is torque split and the only powertrain state is battery SOC.

Due to the lack of a publicly available FE model specific to the 2010 Toyota Prius, the model used was a generic Autonomie power-split HEV model which was modified to represent a 2010 Toyota Prius by setting the following parameters to the publicly available values shown in

Table 6. Parameters and values for the Autonomie 2010 Toyota Prius Model.

Parameter	Value
Overall Vehicle Mass	1530.87 kg
Frontal Area	2.6005 m${}^2$
Coefficient of Drag	0.259
Coefficient of Rolling Resistance	0.008
Wheel Radius	0.317 m
Final Drive Ratio	3.267
Sun Gear Number of Teeth	30
Ring Gear Number of Teeth	78
Battery Open-Circuit Voltage	219.7 V
Battery Internal Resistance	0.373 $\Omega$
Battery Charge Capacity	6.5 Ah

.

Validation of the Autonomie 2010 Prius model was conducted based on publicly available test results from Argonne National Laboratory’s (ANL) Downloadable Dynamometer Database (D${}^3$) [51]. The FE results obtained via the model for three EPA dynamometer drive cycles are compared to those found in D${}^3$ in

Table 7. EPA dynamometer drive cycle FE (km/L) results from the Autonomie 2010 Toyota Prius model and ANL D${}^3$.

Drive Cycle	Data	Model	Percentage Difference
UDDS	32.14	31.79	1.09 %
US06	29.72	30.30	1.95 %
HWFET	19.26	18.98	1.45 %

.

With all modeled FE values within 2% of those found in the ANL D${}^3$ database, the Autonomie 2010 Toyota Prius model was considered validated for further research. It should be noted that, in accorance with physical testing procedure, the initial $SOC$ for the vehicle model was set to fully charged for validation purposes but was set to 50% for furhter research. Thus, FE results for the same EPA dynamometer drive cycles later in the paper with baseline control will be slightly lower than those listed in Table 7.

2.6. System Outputs

In addition to FCDP and PP-MPC, the CV-MPC method was implemented. The CV-MPC method is functionally identical to PP-MPC except that the prediction vector is replaced with a speed vector where all speeds are the current vehicle speed. The CV-MPC method acts as a “null” predictive method which can serve as a point of comparison. The value of a given level of prediction fidelity can be gauged by its performance relative to PP-MPC and CV-MPC. A comparison of the DP-derived methods for a sample drive cycle is shown in Figure 6.

For the sample drive cycle in Figure 6, the FCDP method outperformed the PP-MPC method which outperformed the CV-MPC method and all outperformed the Autonomie baseline control method. Because of the double-sided charge-sustaining penalty, all SOC traces started and ended at exactly $50\%$, which means that fuel consumption can be compared directly without electrical equivalence. For the sample drive cycle, FCDP was able to outperform PP-MPC because it has more freedom to deviate from the start and finish SOC constraints. Generally, the longer the time horizon, the more effective PP-MPC should become. A study was conducted on the UDDS, US06, and HWFET EPA dynamometer drive cycles to demonstrate this. Results for the study are shown in

Table 8. Fuel economy km/L for 2010 Toyota Prius model with DP-derived methods and Autonomie baseline on EPA dynamometer drive cycles (time horizon only effects the PP-MPC and CV-MPC methods).

Drive Cycle	Time Horizon	Baseline	FCDP	PP-MPC	CV-MPC
UDDS	10	28.28	40.32	39.11	35.10
UDDS	15	28.28	40.32	39.45	35.13
UDDS	20	28.28	40.32	39.71	35.00
US06	10	17.57	20.05	18.20	17.50
US06	15	17.57	20.05	18.44	17.20
US06	20	17.57	20.05	18.76	17.21
HWFET	10	28.13	28.59	26.30	24.24
HWFET	15	28.13	28.59	26.56	24.90
HWFET	20	28.13	28.59	26.64	24.37

.

An immediately noticeable trend is that increases in time horizon resulted in better FE for PP-MPC which allowed the PP-MPC FE to approach but not reach the FE produced by the FCDP method. Another noticeable effect is that the relative efficacy of the methods varied between the drive cycles with the DP-derived methods showing massive improvement over baseline in the stop-and-go UDDS drive cycle, while the PP-MPC and CV-MPC methods did not result in FE improvements for the relatively static HWFET drive cycle.

That DP-derived methods present the greatest potential for FE improvement in low-speed stop-and-go conditions is not a surprise. Low-speed stop-and-go conditions are where traditional control methods perform worst as they are unable to operate the IC engine in its most efficient areas. DP methods use knowledge of the future speeds of the vehicle to continue to operate the IC engine efficiently in stop-and-go conditions. An interesting result is that, even with inaccurate information about future vehicle velocity, the CV-MPC method significantly outperformed Autonomie baseline by a significant amount on the UDDS drive cycle.

3. Results

3.1. Direct Analysis of Velocity Prediction Accuracy using MAE

Based on the results of the general study documented in Section 2.3, a second, specific, study was carried out in order to optimize prediction fidelity from LSTM DNNs.

Long Short-Term Memory (LSTM) ANNs are a special case of Recurrent Neural Networks (RNNs) developed by Hochreiter and Schmidhuber [52] which utilize LSTM neurons in hidden layers. While classical recurrent neurons use a single gate to establish the relationship between inputs and outputs, LSTM neurons contain multiple gates which determine how much information should be remembered and forgotten within the neuron as well as the weighting of old and new information. The presence of the remember and forget gates allows LSTM neurons to utilize information from multiple time steps in the past [53,54]. For this reason, LSTM networks are ideally suited for problems where immediate and relayed reactions to inputs are present [55].

Because of its demonstrated feasibility, the LSTM is the prediction model which will be focused on. The following optimal architecture was arrived at:

The LSTM DNN described in

Table 9. Structure of Optimal LSTM DNN.

Layer	Composition
1	Input layer-$n_{inputs}$ fully connected
2	64 LSTM neurons
3	Dropout-10%
4	Batch normalization
5	32 LSTM neurons
6	12 LSTM neurons
7	Output layer-$n_{outputs}$ fully connected

was selected for its high performance and reasonable training time. Adding more complexity to the network past the optimal network failed to generate significant performance gains. The LSTM DNN was trained on the groups of signals defined in

Table 10. Data Groups for LSTM DNN.

Group Label	Composition
A	Speed, Acceleration, Engine Speed, Gear, Steered Angle, Throttle Position, Brake Pressure
B	A + HS + LV
C	A + HS + LV + SPaT + SS

.

The data groups were selected to reflect the data available to different categories of vehicle. A vehicle with neither ADAS nor connectivity only has access to A. Vehicles with ADAS and GPS navigation but no infrastructure connectivity have access to A and B. ICVs have access to all data groups. For groups A, B, and C a cross-validation study was run wherein the LSTM DNN was trained on 9 random laps, validated on 2 random laps, and tested on 2 random laps 30 times. The average MAEs for the cross-validation study are shown in Figure 7. The standard deviations of MAEs were all less than 5% of the mean values.

As is evident in Figure 7, the difference in prediction performance between LSTM DNNs trained on the different data groups was minimal if slightly favoring group B over A and C. A visual comparison of the predictions for all groups at 10 and 20 s is shown in Figure 8.

As the prediction window increases, the LSTM DNN predictions are still able to rougly hold the shape of the velocity trace but produce a greater volume of mis-predictions. The predictions generated using LSTM DNNs trained on the different groups look slightly differently and produce slightly different MAEs but the time horizon length has, by far, the greater impact.

3.2. Overall System FE Output

Using the predictions from the cross validation study mentioned in Section 3.1, FE simulations were conducted using the DP-derived methods and Autonomie baseline controls. The mean FE results for this study are listed in

Table 11. FE (km/L) simulation results based on cross-validation study predictions.

Group Label	Prediction Horizon (s)	Baseline	FCDP	PP-MPC	RP-MPC	CV-MPC
A	10	18.33	24.10	21.78	20.73	20.07
B	10	18.33	24.10	21.78	20.85	20.07
C	10	18.33	24.10	21.78	20.83	20.07
A	15	18.33	24.10	21.87	21.24	20.01
B	15	18.33	24.10	21.87	20.45	20.01
C	15	18.33	24.10	21.87	20.15	20.01
A	20	18.33	24.10	22.22	20.80	20.00
B	20	18.33	24.10	22.22	20.75	20.00
C	20	18.33	24.10	22.22	21.05	20.00

and percentage improvements over baseline for the DP-derived methods with all data groups and at 10, 15, and 20 s are shown in Figure 9.

3.3. Results Summary

The FE results for the DP-derived methods, when taken in conjunction with the results of the LSTM prediction illustrate several trends:

• With perfect predictions MPC methods will produce better FE results for longer prediction horizons.
• A greater volume of mis-predictions will result in worse FE results for MPC methods.
• The small differences in prediction $MAE$ observed between the data groups at all three time horizons are insufficient to explain the large differences observed in FE percentage improvement over baseline for the RP-MPC method between the data groups for the 15 and 20 s horizons.

It is illustrative that, for all cases, the average performance of the RP-MPC method came in between that of the CV-MPC and PP-MPC methods. The PP-MPC method, by definition, produces no mis-predictions while the CV-MPC method, by definition, produces only mis-predictions when the vehicle is moving. It would be logical for the RP-MPC method which produces some degree of mis-prediction to produce FE improvements which are somewhere between those produced by the CV-MPC and RP-MPC methods. The differences in vehicle future velocity prediction $MAE$ between the data groups shown in Figure 7 were relatively small where the differences in FE improvement performance based on those predictions shown in Figure 9 were significant. Furthermore, no consistent trend links the prediction $MAE$ with the percentage FE improvement which leads to the conclusion that $MAE$ is an insufficient metric to describe mis-prediction levels with respect to the RP-MPC method. Further research should be conducted to investigate whether other metrics serve better in this role.

The robustness of DP to velcity prediction error is directly demonstrated in the CV-MPC method which uses a “null” prediction of constant current speed over the entire prediction horizon. It showed significant improvements over baseline while the RP-MPC method showed significant improvements over CV-MPC. An examination of the data trace for all methods using predictions based on group A data for a 10 s prediction horizon are shown in Figure 10.

It can be clearly seen that the MPC methods discover similar local optima, and produce similar optimal state trajectories while the FCDP method, with much more freedom to deviate from the final $SOC$ constraint, takes a substantially different path and ends up using less fuel.

4. Conclusions

In order to to demonstrate the function of various implementations, the data available to different types of vehicle were classified, an extensive real-world driving dataset was collected which incorporated said data, ML and ANN methods were used to predict the ego vehicle future speed using different groups of data, and the best predictions were used in FE simulation to determine the effectiveness of practically implementable POEMS. The results of the velocity prediction study showed that when using a LSTM DNN, high-fidelity velocity prediction was possible using only data which are available to conventional vehicles without ADAS or V2X connectivity and that the addition of ADAS and V2X connectivity resulted in modest fidelity gains. The results of the FE study showed the following:

• FE improvement achievable with RP-MPC approaches and with PP-MPC.
• RP-MPC consistently outperformed CV-MPC.
• Predictions made with ADAS and V2X resulted in greater FE improvement in the 20 s window.

An unavoidable conclusion is that the relationship between prediction fidelity and FE improvement using DP-derived methods cannot be explained by differences in prediction $MAE$.

This study shows that POEMS implementation on HEVs and PHEVs is feasible with causal and implementable prediction and control technologies and would lead to significant improvements in HEV and PHEV fleet efficiency if implemented. The same system architecture as autonomous vehicles (perception, planning, control, plant) can be applied to energy efficiency through the deployment of POEMS-enabled vehicles. The FE improvement which would result is significant and the technology can be implemented currently. The results of this study thus serve as a step towards real-world implementation and commercialization.