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

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Predictive Model for EOP

## 3. Metric for Optimal EOC

#### 3.1. Generic Criteria

#### 3.2. Euclidean Distance—Ideal EOP

#### 3.3. Engine Caliber—Speed and Torque

#### 3.4. Smoothness Measure—EOC Parameters

## 4. Prediction of ACCSSP

#### 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. 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).

#### 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).

#### 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). We incorporated a similar procedure for the next ten seconds, and the ACC Matrix (3X10) was developed (Table 7).

#### 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

#### 5.1. Dataset Retrieval

#### 5.2. Prediction of EOP

#### 5.3. Estimation of Optimal ACCSSP

## 6. Discussion

^{−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.

^{−8}${\mathrm{m}}^{3}$ more fuel in 10 s compared with the predicted ACCSSP.

## 7. Conclusions and Future Work

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ACC | Adaptive cruise control | |

ACCSSP | Adaptive cruise control set speed profile (MPH) | |

Area | Area under the curve | |

AVS | Allowable vehicle speeds | |

CAN | Controller area network | |

CAT | Cabin air temperature (°F) | |

DL | Deep Learning | |

DBV | Driver behaviour vector | |

EAT | External air temperature (°F) | |

ED | Euclidean distance—Ideal EOP and Predicted EOP | |

EOC | Engine operating conditions | |

EOP | Engine operating point | |

ESC | Engine speed caliber | |

EVS | Eligible vehicle speeds | |

ETC | Engine torque caliber | |

FOD | First order derivative | |

IAS | Initial ACC speed (MPH) | |

IEM | Instantaneous engine map | |

IES | Instantaneous engine speed (rad/s) | |

IET | Instantaneous engine torque (Nm) | |

IFCR | Instantaneous fuel consumption rate (1 × 10^{−8} ${\mathrm{m}}^{3}{\mathrm{s}}^{-2}$) | |

ISB | Ideal steering behaviour | |

LAT | Lateral acceleration (m· ${\mathrm{s}}^{-2}$) | |

LOT | Longitudinal acceleration (m·${\mathrm{s}}^{-2}$) | |

LSTM | Long short-term memory | |

GMC | General motors corporation | |

MPH | Miles per hour | |

MY | Model year | |

NARX | Autoregressive network with exogenous inputs | |

OEM | Original equipment manufacturer | |

RMSE | Root mean square error | |

RRC | Radius of road curvature (m) | |

SL | Speed limit (MPH) | |

SNR | Signal to noise ratio | |

SSEStdDev | Sum of squared errorsStandard deviation | |

TP | Tire pressure (kPa) | |

TPFL | Tire pressure front left (kPa) | |

TPFR | Tire pressure front right (kPa) | |

TPRL | Tire pressure rear left (kPa) | |

TPRR | Tire pressure rear right (kPa) | |

VLV | Vehicle level vectors | |

YAR | Yaw rate (rad/s) | |

## Nomenclature

${A}_{c}$ | Area of vehicle cross-section (${\mathrm{m}}^{2}$) |

${C}_{d}$ | Aerodynamic drag coefficient |

°F | Fahrenheit |

g | Gravity |

Hz | Hertz |

kPa | Kilopascals |

Kg | Kilogram |

Km | Kilometres |

kWh | Kilowatt-hour |

${L}_{a\left(k\right)}$ | Lateral acceleration at time step k (m·${\mathrm{s}}^{-2}$) |

${L}_{o\left(k\right)}$ | Longitudinal acceleration at time step k (m·${\mathrm{s}}^{-2}$) |

${M}_{c}$ | Mass of the vehicle. (Kg) |

${M}_{L}$ | Mass of the additional load (Kg) |

MPH | Miles per hour |

m | Meters |

${\mathrm{m}}^{2}$ | Meter square (measure of area) |

${\mathrm{m}}^{3}{\mathrm{s}}^{-1}$ | Meter cube per second (volume rate flow) |

m.${\mathrm{s}}^{-2}$ | Meters per second square |

ms | Milli seconds |

Nm | Newton meter |

${\mu}_{r}$ | Rolling coefficient |

rad | Radians |

rad/s | Radians per second |

$RR{C}_{k}$ | Radius of road curvature at time step k (m) |

RPM | Rotations per minute |

$\rho $ | Density of air (kg.${\mathrm{m}}^{-3}$) |

s | Seconds |

${T}_{k}$ | Timestep |

$dT$ | Incremental time step (~10 ms) |

${\theta}_{g\left(k\right)}$ | Gradient of the terrain at time step k (rad) |

${Y}_{a\left(k\right)}$ | Yaw rate at time step k (rad/s) |

${\mathrm{m}}^{3}{\mathrm{s}}^{-1}$ | Meter cube per second (Volume rate flow) |

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**Figure 1.**Predictive model—inputs and outputs [5].

**Figure 2.**(

**A**) Engine map: 2014 Chevrolet 4.3L; (

**B**) IEM—EOC vector. Environmental Protection Agency, National Vehicle and Fuel Emissions Laboratory, National Center for Advanced Technology, Ann Arbor, Michigan, USA. Version 2018-08.

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 |

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 |

$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 $ $=1.225\mathrm{kg}\xb7{\mathrm{m}}^{-3}$ |

${T}_{k+1}={T}_{k}+dT$ | ${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}$ | $\mathrm{g}=9.81\mathrm{m}\xb7{\mathrm{s}}^{-2}$ |

$T{P}_{k+1}=T{P}_{k}$ | $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 |

Time Step | Odometer (Miles) | Speed (MPH) | RRC (m) | YAR (deg/s) | LAT ($\mathrm{m}\xb7{s}^{-2}$) | LOT ($\mathrm{m}\xb7{s}^{-2}$) |

${T}_{0}$ | 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 |

EOP | Speed | 65 | 66 | 67 | 68 | 69 | 70 | 71 | 72 | 73 | 74 | 75 |

IET | Area | 1.6 × 10^{4} | 3.1 × 10^{4} | 4.7 × 10^{4} | 6.2 × 10^{4} | 7.8 × 10^{4} | 9.4 × 10^{4} | 1.1 × 10^{5} | 1.2 × 10^{5} | 1.4 × 10^{5} | 1.6 × 10^{5} | 1.7 × 10^{5} |

${R}^{2}$ | 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 × 10^{4} | 3.5 × 10^{4} | 5.3 × 10^{4} | 7.1 × 10^{4} | 8.9 × 10^{4} | 1.1 × 10^{5} | 1.2 × 10^{5} | 1.4 × 10^{5} | 1.6 × 10^{5} | 1.8 × 10^{5} | 2.0 × 10^{5} |

${R}^{2}$ | 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 × 10^{4} | 5.6 × 10^{4} | 8.4 × 10^{4} | 1.1 × 10^{5} | 1.4 × 10^{5} | 1.7 × 10^{5} | 1.9 × 10^{5} | 2.2 × 10^{5} | 2.5 × 10^{5} | 2.7 × 10^{5} | 3.0 × 10^{5} |

${R}^{2}$ | 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 × 10^{1} | 1.1 × 10^{2} | 1.6 × 10^{2} | 2.2 × 10^{2} | 2.8 × 10^{2} | 3.3 × 10^{2} | 3.9 × 10^{2} | 4.5 × 10^{2} | 5.0 × 10^{2} | 5.6 × 10^{2} | 6.2 × 10^{2} |

${R}^{2}$ | 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 × 10^{2} | 2.2 × 10^{2} | 3.3 × 10^{2} | 4.5 × 10^{2} | 5.6 × 10^{2} | 6.7 × 10^{2} | 7.8 × 10^{2} | 9.0 × 10^{2} | 1.0 × 10^{3} | 1.1 × 10^{3} | 1.2 × 10^{3} |

${R}^{2}$ | 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 × 10^{4} | 3.7 × 10^{4} | 5.5 × 10^{4} | 7.2 × 10^{4} | 9.0 × 10^{4} | 1.1 × 10^{5} | 1.2 × 10^{5} | 1.4 × 10^{5} | 1.6 × 10^{5} | 1.7 × 10^{5} | 1.9 × 10^{5} |

${R}^{2}$ | 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 |

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 |

${\mathit{T}}_{1}$ | ${\mathit{T}}_{2}$ | ${\mathit{T}}_{3}$ | ${\mathit{T}}_{4}$ | ${\mathit{T}}_{5}$ | ${\mathit{T}}_{6}$ | ${\mathit{T}}_{7}$ | ${\mathit{T}}_{8}$ | ${\mathit{T}}_{9}$ | ${\mathit{T}}_{10}$ |
---|---|---|---|---|---|---|---|---|---|

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 |

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 |

$\mathrm{Acceleration}(\mathrm{m}\xb7{\mathrm{s}}^{-2}$) | 1.090 | 0.652 | 0.598 | 0.808 | 0.449 | 0.556 |

$\mathrm{LOT}(\mathrm{m}\xb7{\mathrm{s}}^{-2}$) | 0.933 | 0.633 | 0.678 | 0.670 | 0.411 | 0.614 |

$\mathrm{LAT}(\mathrm{m}\xb7{\mathrm{s}}^{-2}$) | 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 |

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 |

$\mathrm{Acceleration}(\mathrm{m}\xb7{\mathrm{s}}^{-2}$) | 0.500 | 0.210 | 0.420 | 0.415 | 0.208 | 0.501 |

$\mathrm{LOT}(\mathrm{m}\xb7{\mathrm{s}}^{-2}$) | 0.336 | 0.208 | 0.619 | 0.257 | 0.214 | 0.835 |

$\mathrm{LAT}(\mathrm{m}\xb7{\mathrm{s}}^{-2}$) | 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 |

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 |

$\mathrm{Acceleration}(\mathrm{m}\xb7{\mathrm{s}}^{-2}$) | 0.004 | 0.242 | 67.073 | 0.081 | 0.177 | 2.175 |

$\mathrm{LOT}(\mathrm{m}\xb7{\mathrm{s}}^{-2}$) | −0.091 | 0.188 | −2.079 | 0.108 | 0.189 | 1.748 |

$\mathrm{LAT}(\mathrm{m}\xb7{\mathrm{s}}^{-2}$) | 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 |

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 |

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 |

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 |

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## Share and Cite

**MDPI and ACS Style**

Kolachalama, S.; Malik, H.
Predictive Model of Adaptive Cruise Control Speed to Enhance Engine Operating Conditions. *Vehicles* **2021**, *3*, 749-763.
https://doi.org/10.3390/vehicles3040044

**AMA Style**

Kolachalama S, Malik H.
Predictive Model of Adaptive Cruise Control Speed to Enhance Engine Operating Conditions. *Vehicles*. 2021; 3(4):749-763.
https://doi.org/10.3390/vehicles3040044

**Chicago/Turabian Style**

Kolachalama, Srikanth, and Hafiz Malik.
2021. "Predictive Model of Adaptive Cruise Control Speed to Enhance Engine Operating Conditions" *Vehicles* 3, no. 4: 749-763.
https://doi.org/10.3390/vehicles3040044