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

: 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.


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.
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: Sections 2 and 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.

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.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].

Metric for Optimal EOC
In this section, we defined the metrics for EOC criteria, which reflect optimal EO

Generic Criteria
The predicted EOP for the vehicles traversing the speeds ranging [25 45] MPH rial roads) have a closer proximity to the ideal EOP.In this scenario, the IET has a h magnitude; on the contrary, for the speeds ranging [65 85], MPH (freeways) have h IES recorded.
Additionally, the allowable speeds for the state ways range between [45 65] MPH considered the green zone with maximum fuel economy (low IFCR).Hence, the ge criteria for augmented EOC would include higher IET, higher IES, and lower IFCR, a with the maximum distance traversed for the trip.

Euclidean Distance-Ideal EOP
An engine map calibrated at the manufacturing plant for every model by all aut tive OEM's represents the engine's performance.In general, the ideal EOP for any ve represents the coordinate (centroid) on the map with the lowest IFCR.An example o engine map for the vehicle 2014 Chevrolet 4.3L EcoTec3 LV3 Engine is shown in F 2A.The ideal EOP for this vehicle was estimated to be the coordinate [285 Nm, 2250 R 225 g/kwh].Similarly, the ideal EOPs for the three test vehicles are empirically estim as shown in section A: Table 2.

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

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.

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.
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 ED 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.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  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.

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.

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  /Adjusted  , RMSE, and SSE, using the built-in toolboxes of MATLAB as shown in section B: Table 2.

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.

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.

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

Estimation of Future Input States-DL Model
Step 1: Relative to the current state of the vehicle (VLV k ), the future input values (VLV 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(k+1) ) is estimated based on the vehicle resistance shown in the equation set in Table 3, and the parameters YAR (Y a(k+1) ) and LAT (L a(k+1) ) are calculated assuming ISB (Kolachalama et al., 2018) [25].The environmental parameters EAT k+1 , terrain data, [RRC k+1 , θ g(k) ], are retrieved using the GPS location and the infotainment maps.The magnitudes of the tire pressure (TP k+1 ) and CAT k+1 are assumed to be equal to the previous time step (Table 4).

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

Estimation of Future Input States-DL Model
Step 1: Relative to the current state of the vehicle ( ), the future input values ( ) of the DL model (Figure 3) are estimated using the relations shown in Table 3.The parameter odometer ( ) was calculated using the speed ( ) with the constant time step by basic linear interpolation.The LOT ( ( ) ) is estimated based on the vehicle resistance shown in the equation set in Table 3, and the parameters YAR ( ( ) ) and LAT ( ( ) ) are calculated assuming ISB (Kolachalama et al., 2018) [25].The environmental parameters  , terrain data, [ ,  ( ) ], are retrieved using the GPS location and the infotainment maps.The magnitudes of the tire pressure ( ) and  are assumed to be equal to the previous time step (Table 4).

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).

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).

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].

1.
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 ; 2.
S 1 is chosen closer to S 0 (IAS).If this results in two values, then the higher value is considered as S 1 ; 3.
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 ; 4.
If S k+1 = S k for more than 10 s,

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

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 Tables 8-10.Please find the details of the predictive model in the following sections.

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

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 Tables 4-6.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.

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 m s , 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.

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 m 3 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 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, and R 2 /Adjusted R 2 have similar values (conformance~0), whereas RMSE/SSE have lower
Vehicles 2021,3, 44    traversed by the Cadillac test vehicles.The properties of the six datasets used for this a ysis, including the input and output parameters of the DL model, are shown in Tabl 10.Please find the details of the predictive model in the following sections.