Predictive Model of Adaptive Cruise Control Speed to Enhance Engine Operating Conditions

Abstract

This article presents a novel methodology to predict the optimal adaptive cruise control set speed profile (ACCSSP) by optimizing the engine operating conditions (EOC) considering vehicle level vectors (VLV) (body parameter, environment, driver behaviour) as the affecting parameters. This paper investigates engine operating conditions (EOC) criteria to develop a predictive model of ACCSSP in real-time. We developed a deep learning (DL) model using the NARX method to predict engine operating point (EOP) mapping the VLV. We used real-world field data obtained from Cadillac test vehicles driven by activating the ACC feature for developing the DL model. We used a realistic set of assumptions to estimate the VLV for the future time steps for the range of allowable speed values and applied them at the input of the developed DL model to generate multiple sets of EOP’s. We imposed the defined EOC criteria on these EOPs, and the top three modes of speeds satisfying all the requirements are derived at each second. Thus, three eligible speed values are estimated for each second, and an additional criterion is defined to generate a unique ACCSSP for future time steps. A performance comparison between predicted and constant ACCSSP’s indicates that the predictive model outperforms constant ACCSSP.

1. Introduction

The introduction of automobiles into the world inculcated innovation in many aspects of engineering, including design and manufacturing (Townsend and Calantone, 2014) [1]. Engineers worldwide continuously strive to develop cutting-edge technologies to augment the riders’ comfort, traffic behaviour, enhance safety and fuel economy (Katzenbach, 2015) [2]. In the current scenario, advanced features which include forward collision, traction control, and lane change, augment the safety, whereas the fuel economy drive mode reduces the fuel consumption. Among the features integrated into the vehicle, the ACC system developed by Labuhn and Chundrlik, 1995 played a vital dual role, in affecting safety and EOC [3]. The intricate concept of the ACC system is to produce controlled acceleration without disengaging the cruise in the user-defined proximity and strictly follow the user command of set speed (Marsden et al., 2001) [4]. Additionally, we could conclude from the existing literature (Mahdinia et al., 2020) that the activation of ACC results in lower IFCR [5]. Therefore, activating the ACC feature for traversing long trips would augment EOC.

However, identifying the optimal ACCSSP by considering the dynamic state of the vehicle for a definite coordinate on the terrain is an unsolved, challenging task for engineers. Researchers have performed the parametric optimisation of ACC output in the existing literature by analysing the real-time data of behaviour, traffic congestion, terrain data, and environmental factors. Stanton et al., 2005, Hoedemaeker et al., 1998, Kesting et al., 2007, Rudin-Brown et al., 2004, Moon et al., 2008, and Rosenfeld et al., 2015 considered driver behaviour as the key input to develop the control algorithm using analytical techniques and to tune the outputs of the ACC system [6,7,8,9,10,11]. The enhancements of vehicle connectivity opened doors to obtain real-time traffic congestion information. Milanés et al., 2013:2014, Kesting et al., 2008:2007, and Ploeg et al., 2011, adopted the DL models to estimate the ACCSSP and desired acceleration based on the traffic congestion data retrieved in real-time [12,13,14,15]. Li et al., 2017, Lu et al., 2019, Vedam, 2015, Kolmanovsky and Filev, 2010, Gáspár and Németh, 2014:2011:2013, and Ma et al., 2019, adopted the terrain data to estimate the ACC control parameters to reduce IFCR using the known mathematical models [16,17,18,19,20,21,22,23].

Existing techniques rely on either one or two affecting factors as inputs to predict ACCSSP considered, but none of the researchers included all the factors in conjunction to the best of our knowledge. Recently, we developed a DL model mapping all the VLV and EOP (Kolachalama et al., 2021) [24]. This DL model produced the best results for the ACC activated test case and included all the factors mentioned above, excluding traffic congestion information. This paper applied predefined EOC criteria to the predicted EOP, and the optimal ACCSSP is estimated corresponding to augmented EOC. We validated the proposed model using the real-time test vehicle data-driven road segments that included arterial, state ways, and freeways. The below sections show the detailed procedure adopted.

The rest of the article is organised as follows: Section 2 and Section 4 propose predicting EOP and ACCSSP, whereas Section 3 defines the EOC criteria applied to the EOP to estimate ACCSSP. In Section 5, the detailed results of the predictive model and experimental techniques are presented.

2. Predictive Model for EOP

We adopted the commonly available DL methods, NARX and LSTM, to develop predictive models involving time-sensitive data (Diaconescu, 2008) [25]. Kolachalama et al., 2021, compared NARX and LSTM methods using the real-time test case (2019 Cadillac XT6) and proved that the NARX method outperforms the LSTM model [24]. Hence, in this research, a similar NARX DL model is used with default training options to predict EOP, as shown in

Table 1. Prediction of EOP—NARX DL model.

NARX—Deep Learning Model
Properties		Dataset—Training and Testing
Property	Value	Vehicle	Training	Test Size	ACCSSP (MPH)
Training function	Levenberg–Marquardt backpropagation	2020 Cadillac CT5	1–14,000	14,001–15,000	30
Input/Feedback delays	1:2	2020 Cadillac CT5	1–24,000	24,001–25,000	40
Training, Validation	[30,70]%	2020 Cadillac CT5	1–34,000	34,001–35,000	50
Hidden layer size	10	2020 Cadillac CT5	1–44,000	44,001–45,000	60
Network	Open	2019 Cadillac XT6	1–40,000	40,001–41,000	70
Performance	MSE	2021 Cadillac CT4	1–25,000	25,001–26,000	80

.

As mentioned in the previous section, Figure 1 depicts the DL model to predict the EOP mapping VLV. The outputs of the DL model consist of the elements IET, IES, and IFCR, and the VLV, which embed with driver behaviour, body module parameters, environmental factors, and terrain data. The DBV consists of three elements speeding (Speed, LOT), steering (YAR, LAT) and CAT (Kolachalama et al., 2021) [24,26]. The parameters odometer, tire pressure, curvature, and gradient affect the vehicle traction, whereas CAT and EAT influence thermal stress on the engine (Kolachalama et al., 2008) [27]. Additionally, there is no loss of generality in replacing the gradient with the vehicle posture’s Euler angles, which affect the traction under no-slip (Eathakota et al., 2010) [28,29].

3. Metric for Optimal EOC

In this section, we defined the metrics for EOC criteria, which reflect optimal EOP.

3.1. Generic Criteria

The predicted EOP for the vehicles traversing the speeds ranging [25 45] MPH (arterial roads) have a closer proximity to the ideal EOP. In this scenario, the IET has a higher magnitude; on the contrary, for the speeds ranging [65 85], MPH (freeways) have higher IES recorded.

Additionally, the allowable speeds for the state ways range between [45 65] MPH are considered the green zone with maximum fuel economy (low IFCR). Hence, the generic criteria for augmented EOC would include higher IET, higher IES, and lower IFCR, along with the maximum distance traversed for the trip.

3.2. Euclidean Distance—Ideal EOP

An engine map calibrated at the manufacturing plant for every model by all automotive OEM’s represents the engine’s performance. In general, the ideal EOP for any vehicle represents the coordinate (centroid) on the map with the lowest IFCR. An example of the engine map for the vehicle 2014 Chevrolet 4.3L EcoTec3 LV3 Engine is shown in Figure 2A. The ideal EOP for this vehicle was estimated to be the coordinate [285 Nm, 2250 RPM, 225 g/kwh]. Similarly, the ideal EOPs for the three test vehicles are empirically estimated, as shown in section A:

Table 2. EOC criteria—EOP.

Section A				Section B
Ideal EOP				Generic		Engine Specific		Smoothness Measure—Spline Fit
Vehicle	IET (Nm)	IES (rad/s)	IFCR $(1 \times {10}^{-8} {\mathrm{m}}^3{\mathrm{s}}^{-1})$	Parameter	Condition	Parameter	Condition	Parameter	Condition
Cadillac CT5	250	140	180	IET	Higher	ED	Lower	$R^2$$/\mathrm{Adj} R^2$	Higher
Cadillac XT6	280	145	220	IES	Higher	ESC	Higher	RMSE	Lower
Cadillac CT4	240	140	200	IFCR	Lower	ETC	Higher	SSE	Lower

.

Hence, we defined the line segment conjoining the predicted and ideal EOP as the EOC vector, represented by the IEM shown in Figure 2B. The magnitude of the EOC vector represents the $E{D}_i$ shown in Equation (1). In the 2D plane, there is no loss of generality in ignoring the parameter IES, as it is proportional to the vehicle speed. Therefore, lower ED represents increased EOC.

$$E{D}_i=\sqrt{ {\left(IE{T}_i-IE{T}_k\right)}^2+{\left(IFC{R}_i-IFC{R}_k\right)}^2 }$$

(1)

3.3. Engine Caliber—Speed and Torque

The engine’s capability is measured by two standard parameters [ESC, ETC]. These parameters are the ratios that define the torque produced per unit of fuel consumption and the speed produced per unit of torque. Higher ETC and ESC are the desired criteria for every vehicle’s trip.

$$\mathrm{ETC}=\frac{IET}{IFCR}$$

(2)

$$\mathrm{ESC}=\frac{IES}{IET}$$

(3)

3.4. Smoothness Measure—EOC Parameters

The combustion of fuel in the engine produces torque with fluctuating magnitudes. However, all the elements of EOP should have smooth behaviour (Tanaka et al., 1987, Li et al., 2017) [30,31]. Hence, as an additional optimal EOC metric, we defined the smoothness measure for all the six parameters—IET, IES, IFCR, ED, ETC, ESC. We used the spline to fit the data points of EOC parameters by normalising the data. The optimal fit criteria were measured by traditional statistical techniques $R^2$/Adjusted $R^2$, RMSE, and SSE, using the built-in toolboxes of MATLAB as shown in section B: Table 2.

4. Prediction of ACCSSP

The prediction of ACCSSP was categorised into four steps, as described in the following sections.

4.1. Estimation of Future Input States—DL Model

Step 1: Relative to the current state of the vehicle ($VL{V}_k$), the future input values ($VL{V}_{k+1}$) of the DL model (Figure 3) are estimated using the relations shown in

Table 3. Equation set—prediction of future input states.

$RR{C}_{k+1}$$, {\theta }_{g\left(k+1\right)}$	$2RR{C}_{k+1}=\frac{S_{k+1}^2}{L_{a\left(k+1\right)} }+\frac{S_{k+1}}{Y_{a\left(k+1\right)}}$$, min \left[abs\left(Y_{a\left(k+1\right)}.S_{k+1}-L_{a\left(k+1\right)}\right)\right]$	$\rho$  $= 1.225 \mathrm{kg}·{\mathrm{m}}^{-3}$
$T_{k+1}=T_k+dT$	$L_{o\left(k+1\right)}=$$g{\mu }_r$$+gsin({\theta }_{g\left(k+1\right)})$$+\frac{\rho C_d.A_c}{2.\left(M_c+M_L\right)}$$.S_{k+1}^2$	$S_{k+1}=\left[SL-10, SL\right]$
$O_{k+1}=O_k+S_k.dT$	$2020 \mathrm{Cadillac} \mathrm{CT}5: M_c$$=1769.69 \mathrm{kg}, M_L$$=76.8 \mathrm{kg},C_d$$=0.31, \mathrm{A}=1.71 {\mathrm{m}}^2$	$CA{T}_{k+1}=CA{T}_k$
$EA{T}_{k+1}=EA{T}_k$	$2019 \mathrm{Cadillac} \mathrm{XT}6: M_c$$=2050.278 \mathrm{kg}, M_L$$=76.8 \mathrm{kg}, C_d$$=0.35, \mathrm{A}=1.88 {\mathrm{m}}^2$	$\mathrm{g}=9.81 \mathrm{m}·{\mathrm{s}}^{-2}$
$T{P}_{k+1}=T{P}_k$	$2021 \mathrm{Cadillac} \mathrm{CT}4: M_c$$=1626.94 \mathrm{kg}, M_L$$=76.8 \mathrm{kg}, C_d$$=0.30, \mathrm{A}=1.70{ \mathrm{m}}^2$	${\mu }_r$= 0.013

. The parameter odometer ($O_{k+1}$) was calculated using the speed ($S_k$) with the constant time step by basic linear interpolation. The LOT ($L_{o\left(k+1\right)}$) is estimated based on the vehicle resistance shown in the equation set in Table 3, and the parameters YAR ($Y_{a\left(k+1\right)}$) and LAT ($L_{a\left(k+1\right)}$) are calculated assuming ISB (Kolachalama et al., 2018) [25]. The environmental parameters $EA{T}_{k+1}$, terrain data, [$RR{C}_{k+1}$, ${\theta }_{g\left(k\right)}$], are retrieved using the GPS location and the infotainment maps. The magnitudes of the tire pressure ($T{P}_{k+1}$) and $CA{T}_{k+1}$ are assumed to be equal to the previous time step (

Table 4. Predicted inputs—DL model, 2019 Cadillac XT6 (100 time steps = 1 s).

Time Step	Odometer (Miles)	Speed (MPH)	RRC (m)	YAR (deg/s)	LAT ($\mathrm{m}·s^{-2}$)	LOT ($\mathrm{m}·s^{-2}$)
$T_0$	15,000	70	8304.140	0.216	0.117	0.437
$d{T}_{10}$	15,000.001	70	8304.140	0.216	0.117	0.375
$d{T}_{20}$	15,000.003	70	8304.140	0.216	0.117	0.312
$d{T}_{30}$	15,000.005	70	9342.157	0.192	0.104	−0.125
$d{T}_{40}$	15,000.007	70	24,912.42	0.072	0.039	−0.187
$d{T}_{50}$	15,000.009	70	74,737.261	0.024	0.013	−0.062
$d{T}_{60}$	15,000.011	70	74,737.261	0.024	0.013	0.25
$d{T}_{70}$	15,000.013	70	37,368.630	0.048	0.026	0.25
$d{T}_{80}$	15,000.015	70	24,912.420	0.072	0.039	0.187
$d{T}_{90}$	15,000.017	70	24,912.420	0.072	0.039	0.187
$T_1$	15,000.019	70	9342.157	0.192	0.104	0.312

).

4.2. Prediction of Outputs—DL Model

Step 2: We estimated the input sets for future time steps (1 s—[$T_0$ $T_1$]) for the AVS range (e.g., [SL-10, SL]). Thus, we generated eleven sets of inputs, and fed them into the DL model, and predicted a corresponding eleven sets of outputs (EOP’s) (

Table 5. EOC criteria—iteration of ACC Speeds (100 time steps).

EOP	Speed	65	66	67	68	69	70	71	72	73	74	75
IET	Area	1.6 × 104	3.1 × 104	4.7 × 104	6.2 × 104	7.8 × 104	9.4 × 104	1.1 × 105	1.2 × 105	1.4 × 105	1.6 × 105	1.7 × 105
	$R^2$	0.76	0.83	0.77	0.74	0.77	0.77	0.75	0.77	0.75	0.78	0.76
	$\mathrm{Adj} R^2$	0.4	0.57	0.43	0.36	0.44	0.43	0.39	0.44	0.37	0.44	0.4
	SSE	6.26	4.47	5.94	6.69	5.82	5.94	6.34	5.76	6.49	5.72	6.16
	RMS	0.4	0.33	0.39	0.41	0.38	0.38	0.4	0.38	0.4	0.38	0.39
IES	Area	1.8 × 104	3.5 × 104	5.3 × 104	7.1 × 104	8.9 × 104	1.1 × 105	1.2 × 105	1.4 × 105	1.6 × 105	1.8 × 105	2.0 × 105
	$R^2$	1	1	1	1	1	1	1	1	1	1	1
	$\mathrm{Adj} R^2$	0.99	0.99	0.99	0.99	0.99	0.99	0.99	0.99	1	0.99	0.99
	SSE	0.003	0.002	0.003	0.003	0.003	0.003	0.002	0.001	0.001	0.001	0.001
	RMS	0.009	0.007	0.008	0.008	0.009	0.008	0.007	0.006	0.005	0.006	0.006
IFCR	Area	2.8 × 104	5.6 × 104	8.4 × 104	1.1 × 105	1.4 × 105	1.7 × 105	1.9 × 105	2.2 × 105	2.5 × 105	2.7 × 105	3.0 × 105
	$R^2$	0.78	0.78	0.72	0.74	0.8	0.75	0.81	0.74	0.76	0.68	0.67
	$\mathrm{Adj} R^2$	0.46	0.45	0.31	0.35	0.5	0.37	0.53	0.36	0.4	0.22	0.17
	SSE	4913.31	4737.99	5613.29	4967.08	3726.95	4633.05	3429.65	4679.59	4418.54	5766.31	6140.52
	RMS	11.19	10.99	11.97	11.26	9.75	10.85	9.35	10.92	10.62	12.13	12.52
ETC	Area	5.4 × 101	1.1 × 102	1.6 × 102	2.2 × 102	2.8 × 102	3.3 × 102	3.9 × 102	4.5 × 102	5.0 × 102	5.6 × 102	6.2 × 102
	$R^2$	0.788	0.781	0.724	0.739	0.802	0.751	0.814	0.745	0.759	0.689	0.671
	$\mathrm{Adj} R^2$	0.469	0.452	0.309	0.348	0.504	0.377	0.535	0.362	0.398	0.222	0.176
	SSE	0.02	0.02	0.025	0.023	0.017	0.022	0.016	0.023	0.022	0.03	0.033
	RMS	0.022	0.023	0.025	0.024	0.021	0.023	0.02	0.024	0.024	0.028	0.029
ESC	Area	1.1 × 102	2.2 × 102	3.3 × 102	4.5 × 102	5.6 × 102	6.7 × 102	7.8 × 102	9.0 × 102	1.0 × 103	1.1 × 103	1.2 × 103
	$R^2$	0.822	0.869	0.824	0.801	0.826	0.817	0.799	0.812	0.783	0.807	0.792
	$\mathrm{Adj} R^2$	0.554	0.672	0.56	0.503	0.565	0.542	0.497	0.529	0.457	0.517	0.479
	SSE	0	0	0	0	0	0	0	0	0	0	0
	RMS	0.003	0.002	0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.003
ED	Area	1.9 × 104	3.7 × 104	5.5 × 104	7.2 × 104	9.0 × 104	1.1 × 105	1.2 × 105	1.4 × 105	1.6 × 105	1.7 × 105	1.9 × 105
	$R^2$	0.787	0.783	0.725	0.743	0.802	0.751	0.815	0.747	0.761	0.689	0.671
	$\mathrm{Adj} R^2$	0.467	0.457	0.311	0.358	0.504	0.378	0.538	0.368	0.402	0.222	0.176
	SSE	4896.87	4721.42	5595.32	4950.75	3716.68	4620.39	3421.22	4665.06	4404.92	5749.95	6123.26
	RMS	11.18	10.978	11.951	11.241	9.74	10.86	9.345	10.912	10.604	12.115	12.502

).

4.3. Estimation of ACC Speed Values—EOC Criteria

Step 3: We applied the EOC criteria defined in section III for the eleven predicted EOP’s (Table 5). The top six performing speed values are selected for each EOC parameter, and hence, the top three modes of speeds (EVS) are calculated for each time step (

Table 6. Eligible ACC speeds—EOC criteria (100 time steps = 1 s).

Area	$R^2$	$\mathrm{Adj} R^2$	SSE	RMS	Area	$R^2$	$\mathrm{Adj} R^2$	SSE	RMS	Area	$R^2$	$\mathrm{Adj} R^2$	SSE	RMS
IE					IES					IFCR
75	69	69	70	70	75	68	68	75	75	65	66	66	75	75
74	70	70	69	69	74	71	71	71	71	66	69	69	66	66
73	65	65	71	71	73	70	70	68	68	67	75	75	69	69
72	68	68	72	72	72	69	69	70	70	68	65	65	65	65
71	71	71	68	68	71	67	67	72	72	69	70	70	70	70
70	73	73	73	73	70	72	72	74	74	70	67	67	72	72
ETC					ESC					ED
75	66	66	66	66	75	69	69	70	70	65	66	66	75	75
74	69	69	65	65	74	70	70	69	69	66	69	69	66	66
73	75	75	69	69	73	68	68	71	71	67	75	75	69	69
72	65	65	75	75	72	65	65	72	72	68	65	65	70	70
71	70	70	70	70	71	71	71	73	73	69	70	70	65	65
70	67	67	67	67	70	66	66	68	68	70	67	67	72	72

). We incorporated a similar procedure for the next ten seconds, and the ACC Matrix (3X10) was developed (

Table 7. ACC speeds—10 s, SL = 75 MPH.

${\mathit{T}}_1$	${\mathit{T}}_2$	${\mathit{T}}_3$	${\mathit{T}}_4$	${\mathit{T}}_5$	${\mathit{T}}_6$	${\mathit{T}}_7$	${\mathit{T}}_8$	${\mathit{T}}_9$	${\mathit{T}}_{10}$
69	68	66	75	74	67	67	75	67	75
71	70	65	68	72	71	72	66	75	71
68	71	67	65	65	74	73	68	73	65

).

4.4. Algorithm to Predict ACCSSP

Step 4: Every second has three EVS, resulting in a maximum of $3^{10}$ possible ACCSSP’s for 10 s. The following conditions are defined to identify a unique ACCSSP inspired by the Dubin path traverse problem (La Valle, 2011) [32].

• Assuming the ACCSSP at $T_k$ is $S_k$, if the EVS is either $S_k$+1, $S_k$, or $S_k$−1, the highest magnitude among the three is selected as $S_{k+1}$;
• $S_1$ is chosen closer to $S_0$ (IAS). If this results in two values, then the higher value is considered as $S_1$;
• If the eligible speeds at $T_{k+1}$ are neither $S_k$+ 1, $S_k$, nor $S_k$ − 1, then $S_{k+1}=S_k$;
• If $S_{k+1}=S_k$ for more than 10 s, $S_{k+1}$= $S_k$+ 1 if $S_k$+ 1 $\le$ SL or $S_k$ − 1 if $S_k$= SL.

5. Experimental Results

A series of experiments are designed, analysed and evaluated on a real-time dataset to evaluate the performance of the proposed framework.

5.1. Dataset Retrieval

We conducted this research using three test vehicles, a 2019 Cadillac XT6, a 2020 Cadillac CT5, and a 2021 Cadillac CT4, obtained from GMC. A two-step procedure was employed to retrieve the data from the vehicle CAN bus (Li et al., 2008) [33]. We connected the hardware neoVI to the vehicle and retrieved the data retrieval using the software Vehicle Spy. This tool records data in real-time (Gallardo, 2018) and allows the user to selectively retrieve the signal data required for analysis [34]. We performed the real-time test procedure by activating the ACC feature, and time-step snippets of data were collected for each vehicle at a frequency of 10 Hz, i.e., 100 data points are recorded for 1s assuming a no-slip (Eathakota et al., 2008) [28,29].

The test cases are developed by driving the vehicles on selected road segments covering all the arterial, state ways, and freeways scenarios. Shown in Figure 4 are the paths traversed by the Cadillac test vehicles. The properties of the six datasets used for this analysis, including the input and output parameters of the DL model, are shown in

Table 8. Data Set 1: 2020 Cadillac CT5—arterial roads.

Parameters	ACC Speed [25 35] MPH			ACC Speed [35 45] MPH
Inputs	Mean	StdDev	Variance	Mean	StdDev	Variance
Absolute time (s)	2468.020	1655.047	0.671	4584.239	2453.828	0.535
Odometer (km)	11,721.440	41.765	0.004	11,596.730	56.886	0.005
Speed (MPH)	30.831	2.859	0.093	40.634	2.768	0.068
$\mathrm{Acceleration} (\mathrm{m}·{\mathrm{s}}^{-2}$)	1.090	0.652	0.598	0.808	0.449	0.556
$\mathrm{LOT} (\mathrm{m}·{\mathrm{s}}^{-2}$)	0.933	0.633	0.678	0.670	0.411	0.614
$\mathrm{LAT} (\mathrm{m}·{\mathrm{s}}^{-2}$)	0.318	0.637	2.002	0.362	0.335	0.924
YAR (deg/s)	0.098	2.633	26.944	0.179	1.056	5.914
EAT (°F)	12.964	0.688	0.053	14.727	1.742	0.118
CAT (°F)	66.141	0.348	0.005	68.895	1.069	0.016
TPFL (kPa)	225.908	2.915	0.013	226.990	3.243	0.014
TPRL (kPa)	235.773	4.640	0.020	239.900	4.259	0.018
TPFR (kPa)	235.115	4.834	0.021	235.575	3.706	0.016
TPRR (kPa)	234.132	5.742	0.025	237.544	4.270	0.018
Outputs	Mean	StdDev	Variance	Mean	StdDev	Variance
IET (Nm)	173.081	45.424	0.262	186.309	30.686	0.165
IES (rad/s)	219.483	82.421	0.376	222.809	73.464	0.330
$\mathrm{IFCR} (1 \times {10}^{-8} {\mathrm{m}}^3{\mathrm{s}}^{-1}$)	380.687	204.214	0.536	378.523	139.192	0.368

,

Table 9. Data Set 2: 2020 Cadillac CT5—state ways roads.

Parameters	ACC Speed [45 55] MPH			ACC Speed [55 65] MPH
Inputs	Mean	StdDev	Variance	Mean	StdDev	Variance
Absolute time (s)	3701.490	1808.730	0.489	2933.845	1442.236	0.492
Odometer (km)	11,410.820	42.130	0.004	11,894.840	36.372	0.003
Speed (MPH)	51.354	2.605	0.051	60.707	2.821	0.046
$\mathrm{Acceleration} (\mathrm{m}·{\mathrm{s}}^{-2}$)	0.500	0.210	0.420	0.415	0.208	0.501
$\mathrm{LOT} (\mathrm{m}·{\mathrm{s}}^{-2}$)	0.336	0.208	0.619	0.257	0.214	0.835
$\mathrm{LAT} (\mathrm{m}·{\mathrm{s}}^{-2}$)	0.256	0.193	0.751	0.305	0.180	0.590
YAR (deg/s)	−0.190	0.534	−2.805	−0.030	0.473	−15.914
EAT (°F)	12.889	0.556	0.043	15.083	0.670	0.044
CAT (°F)	69.726	0.688	0.010	66.000	0.000	0.000
TPFL (kPa)	235.424	3.508	0.015	239.108	2.371	0.010
TPRL (kPa)	233.685	3.947	0.017	237.436	2.193	0.009
TPFR (kPa)	226.567	3.062	0.014	228.252	0.972	0.004
TPRR (kPa)	233.767	3.764	0.016	238.294	2.279	0.010
Outputs	Mean	StdDev	Variance	Mean	StdDev	Variance
IET (Nm)	234.943	25.244	0.107	254.370	27.752	0.109
IES (rad/s)	167.982	28.195	0.168	180.272	36.291	0.201
$\mathrm{IFCR} (1 \times {10}^{-8} {\mathrm{m}}^3{\mathrm{s}}^{-1}$)	374.715	82.660	0.221	441.351	109.691	0.249

and

Table 10. Data Set 3: 2019 Cadillac XT6, 2021 Cadillac CT4—freeways roads.

Parameters	Cadillac XT6, ACC Speed [65 75] MPH			Cadillac CT4, ACC Speed [75 85] MPH
Inputs	Mean	StdDev	Variance	Mean	StdDev	Variance
Absolute time (s)	387.430	223.687	0.577	31.709	12.962	0.409
Odometer (km)	12,723.040	7.015	0.001	30,298.330	17.042	0.001
Speed (MPH)	70.121	1.149	0.016	77.905	1.501	0.019
$\mathrm{Acceleration} (\mathrm{m}·{\mathrm{s}}^{-2}$)	0.004	0.242	67.073	0.081	0.177	2.175
$\mathrm{LOT} (\mathrm{m}·{\mathrm{s}}^{-2}$)	−0.091	0.188	−2.079	0.108	0.189	1.748
$\mathrm{LAT} (\mathrm{m}·{\mathrm{s}}^{-2}$)	0.132	0.339	2.572	−0.149	0.307	−2.057
YAR (deg/s)	0.230	0.851	3.698	−0.256	0.694	−2.710
EAT (°F)	39.225	0.296	0.008	85.039	0.998	0.012
CAT (°F)	68.785	0.301	0.004	66.502	0.862	0.013
Pitch angle (deg)	−0.262	0.742	−2.836	−0.003	0.002	−0.771
TPFL (kPa)	241.238	2.428	0.010	227.807	0.289	0.001
TPRL (kPa)	235.890	0.655	0.003	249.502	0.290	0.001
TPFR (kPa)	243.691	1.069	0.004	228.316	0.409	0.002
TPRR (kPa)	235.224	1.582	0.007	249.503	0.287	0.001
Outputs	Mean	StdDev	Variation	Mean	StdDev	Variance
IET (Nm)	146.803	63.428	0.432	142.117	33.698	0.237
IES (rad/s)	183.081	7.105	0.039	205.343	17.341	0.084
$\mathrm{IFCR} (1 \times {10}^{-8} {\mathrm{m}}^3{\mathrm{s}}^{-1}$)	387.430	223.687	0.577	31.709	12.962	0.409

. Please find the details of the predictive model in the following sections.

5.2. Prediction of EOP

The properties of the NARX model and the test cases used for training are shown in Table 1. We developed individual training networks with default properties using the DL toolbox of MATLAB for the three vehicles’ test data and the predicted EOP’s, as shown in the Supplementary Materials, Figures S1–S6. Each figure consists of three parts: IET (left), IES (middle), and IFCR (right). Furthermore, each plot compares the measured data (blue) with the predicted values (orange). We validated the performance of the NARX DL model prediction using traditional statistical techniques (RMSE, FOD, SNR) to compare the actual and predicted values of EOP, as reported in

Table 11. NARX DL model performance—ACCSSP [30 80] MPH.

EOP	IET			IES			IFCR
Metric	RMSE	FOD	SNR	RMSE	FOD	SNR	RMSE	FOD	SNR
30 MPH	2.761	1.911	35.003	2.367	1.541	35.417	12.911	8.717	25.499
40 MPH	0.750	0.418	45.362	0.845	0.484	37.442	14.122	9.477	24.418
50 MPH	1.263	0.811	45.566	1.400	0.932	43.413	18.966	13.289	25.495
60 MPH	0.590	0.417	51.103	0.521	0.348	51.414	21.740	15.241	25.582
70 MPH	0.322	0.186	53.762	0.228	0.169	58.007	8.335	5.877	30.369
80 MPH	0.576	0.618	46.651	0.064	0.027	70.160	9.917	6.879	27.586

. We conclude that IES follows a smooth curve, whereas IFCR and IET oscillate.

5.3. Estimation of Optimal ACCSSP

The developed DL model and the steps defined in Section 4 are used to estimate the optimal ACCSSP for each test case. An example, for the test case of the vehicle 2019 Cadillac XT6, is selected with the AVS = [65 75] MPH, and the corresponding results are shown in Table 4, Table 5 and Table 6. The IAS ($S_0$) is varied in the range [65 75] MPH for the ACC Matrix (Table 7), and Step 4 is applied to the EVS, which results in eight ACCSSP’s shown in Figure 5. Thus for $S_0$ = 70 MPH, the predicted ACCSSP is the row vector ((71, 71, 71, 71, 72, 72, 73, 73, 74, 74) MPH) as shown in Figure S8. We adopted a similar procedure for multiple data sets and plotted the predicted ACCSSP’s are presented in the Supplementary Materials, Figures S7–S12. Please find the performance of EOC parameters for the predicted ACCSSP’s in Section B:

Table 12. EOC criteria: engine parameters (predicted–constant) ACCSSP.

Section: A				Section: B
Data	IAS = 70 MPH, SL = 75 MPH			Speed (MPH)		Test Cases
Metric	ACCSSP (70 MPH)	ACCSSP (Predicted)	Conformance	SL	IAS	Distance	ED	IFCR	ETC	ESC
				35	30	0.22	−17.33	−21.19	0.25	−0.26
Distance	69,930.00	72,028.00	934.77	45	40	133.44	−64.11	−52.113	−0.27	0.50
ED	17,4570.83	17,4196.86	−373.96	55	50	712.22	−366.13	−323.27	0.51	1.20
ETC	572.12	573.34	1.22	65	60	−312.11	−510.75	−540.58	0.87	0.22
ESC	1154.63	1164.83	10.20	75	70	934.77	−373.96	−379.09	1.22	10.20
IFCR	27,4182.80	27,3803.70	−379.09	85	80	801.108	−1035.28	−1029.6	2.813	−2.022

.

6. Discussion

The plots of predicted EOP’s for the three test vehicles Cadillac CT5, XT6, and CT4, are depicted in Figures S1–S6 The predictive model is validated by estimating the conformance between actual and predicted data’s RMSE, FOD, and SNR (Table 11). The IET RMSE values were <2.76, whereas IES FOD was <1.54 for all the datasets. We recorded the IFCR on a scale of 1 × 10⁻⁸ ${\mathrm{m}}^3{\mathrm{s}}^{-1}$, and the IFCR SNR has an acceptable range of [24.41–30.36]. Additionally, we can visualise that the predicted curves have a smoother fit to the actual data, and thus efficacy of the DL model to predict EOP is validated.

In this work, we proposed the criteria for augmented EOC and an iterative methodology to predict ACCSSP’s, resulting in optimal EOP. Hence, for each future second, the AVS is varied in a definite range [65 75] MPH for the 2019 Cadillac XT6, and the corresponding inputs for the future states are fed into the DL model to generate multiple EOPs. We applied EOC criteria to the EOPs, and the top three EVS are estimated as [69,71,68] MPH.

We adopted a similar procedure for ten seconds and predicted ACCSSP for IAS = 70 MPH, SL = 75 MPH, with a minimum of 71 MPH and a maximum of 73 MPH (Figure S8). The predicted and constant ACCSSP profile (70 MPH) with corresponding inputs (Section 4.1) were fed into the DL model to obtain two different EOP’s vectors (Section 4.2) for future time steps (10 s). We applied the EOC criteria for the two EOPs whose values are in Section A: Table 12 and thus predicted ACCSSP resulted in 934.77 m of the additional distance traversed and a reduced ED of 373.968. Additionally, the constant ACCSSP = 70 MPH consumed 379.095 1 × 10⁻⁸ ${\mathrm{m}}^3$ more fuel in 10 s compared with the predicted ACCSSP.

The plots of engine performance parameters are shown in Figure 6, and the area under the curve has higher magnitudes by 1.2 (ETC) and 10.2 (ESC) for the predicted ACCSSP. Please find the smoothness measure for the conformance of the two EOP’s in

Table 13. EOC criteria: smoothness performance—(predicted–constant) ACCSSP.

EOP		IET				IES				IFCR
SL	IAS	${\mathit{R}}^2$	$\mathbf{Adj} {\mathit{R}}^2$	SSE	RMS	${\mathit{R}}^2$	$\mathbf{Adj} {\mathit{R}}^2$	SSE	RMS	${\mathit{R}}^2$	Adj ${\mathit{R}}^2$	SSE	RMS
35	30	0.0	0.0	−9.415	−0.007	0.0	0.000	0.564	0.000	0.000	0.0	−103.786	−0.023
45	40	0.0	0.0	0.326	0.001	0.0	0.000	2.582	0.013	0.000	0.0	−23.251	−0.005
55	50	0.0	0.0	3.069	0.007	0.0	0.001	−38.090	−0.033	0.000	0.0	−570.595	−0.083
65	60	0.0	0.0	1.307	0.005	0.0	0.000	0.431	0.002	0.000	0.0	33.212	0.004
75	70	0.0	0.0	0.368	0.004	0.064	0.160	−2.607	−0.024	0.000	0.0	136.612	0.044
85	80	0.0	0.0	−0.312	−0.001	−0.002	−0.005	0.142	0.007	0.001	0.002	−243.889	−0.068

, and $R^2$/Adjusted $R^2$ have similar values (conformance~ 0), whereas RMSE/SSE have lower values for predicted ACCSSP for most cases. Section B: Table 12 depicts the performance of EOC parameters for all the test cases, and it is easy to see that in most cases, the predicted ACCSSP has reduced ED and IFCR. Hence the proposed approach in this article is novel and better suits enhancing EOC and lowering the trip time.

7. Conclusions and Future Work

In this manuscript, we developed a novel method to predict the ACCSSP, which optimises engine performance. We considered the vector EOP and used NARX DL modelling techniques to predict the EOP by mapping the VLV. We defined EOC criteria using the elements of EOP, which reflect enhanced engine operating conditions. In this methodology, a new approach of inputting the range of allowable ACC speeds is proposed and, therefore, a unique ACCSSP for the future time-steps was generated in the defined range by utilising iterative methods and satisfying the EOC criteria. The predicted and constant ACCSSP are fed into the DL model, and the engine performance parameters are estimated based on the predicted EOP. The results depict that for predicted ACCSSP, the parameters (ETC, ESC, IET, IES), and (IFCR, ED) have higher and lower values. Additionally, the predicted ACCSSP generated smoother profiles for the engine parameters when plotted in the time domain.

The researchers have not investigated the proposed technique of predicting ACCSSP, and this new approach could also trigger a new capability in ACC controllers to deviate from the user command of unique set speed and produce enhanced vehicle performance. The computational results obtained were satisfactory, and thus, we observed augmented EOC for the predicted ACCSSP.

We did not include many critical points, including traffic congestion, in the model. Future work would involve developing the model by including all the affecting parameters and performing extensive validation using multiple vehicle lines at various locations and periods. Additionally, this research could be extended to electric vehicles by defining new criteria of battery and motor operating conditions.