Driver Model Based on Optimized Calculation and Functional Safety Simulation

energies

Article Driver Model Based on Optimized Calculation and Functional Safety Simulation

Zhaolong Zhang 1, Yuan Zou 1,*, Xudong Zhang 1, Zhifeng Xu 2 and Han Wang 1 1 School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081, China; [email protected] (Z.Z.); [email protected] (X.Z.); [email protected] (H.W.) 2 Beijing Electric Vehicle Co. Ltd., Beijing 102606, China; [email protected] * Correspondence: [email protected]

Received: 3 November 2020; Accepted: 15 December 2020; Published: 17 December 2020

Abstract: The simulation of electronic control function failure has been utilized broadly as an evaluation method when determining the Automotive Safety Integrity Level (ASIL). The driver model is quite critical in the ASIL evaluation simulation. A new driver model that can consider drivers of diﬀerent driving skills is proposed in this paper. It can simulate the overall performance of diﬀerent drivers driving vehicles by adjusting parameters, with which the impact of a certain electronic control function failure and the ASIL are evaluated. This paper has taken the function failure of regenerative braking as the simulation object in the double-lane-change driving scenario to simulate typical driving conditions with the designed driver model, and then has obtained the ASIL of regenerative braking function, which is applied to a BAIC new energy vehicle development project.

Keywords: electric vehicle; functional safety; vehicle dynamics simulation

1. Introduction More and more electronic control functions have been integrated into vehicles with the improvement of vehicle electrification in recent years [1]. In order to ensure vehicle safety, functional safety design should be taken into consideration for the electronic control system [2–4]. A functional safety rating is the key to functional safety design. When assessing the functional safety level, it is necessary to simulate the potential accidents caused by the electronic control function failure regarding the controllability, severity, and fault tolerance time [5,6]. To simulate electronic control function failure and its effect, the most widely used method is by computer simulation, which uses a virtual model of the “driver-vehicle-environment” system [7] to obtain the final data under different dangerous driving conditions. The driver, vehicle, and environment sub-models should be as close as possible to the real situation in the abovementioned virtual model. At present, the design technology of vehicle and environment sub-models is relatively mature, while the research of driver sub-model applied to Automotive Safety Integrity Level (ASIL) simulation is still in the early phase. One of the design difficulties is how to design a reliable model that can simulate drivers with different driving skills to improve the simulation results. When driving the vehicle, the driver firstly decides the target route which is to be tracked by turning the steering wheel based on the experience of the vehicle’s steering characteristics, while maintaining vehicle stability. Existing research shows that when the steering wheel is turned by different drivers there are two critical parameters—vehicle lateral displacement and yaw angle status [8–10]. For drivers with poor driving experience, the vehicle is equivalent to a particle, so that more consideration is given to whether the vehicle displacement is consistent with driver expectations. Drivers with significant driving experience pay more attention to the smooth adjustment of the vehicle’s yaw status to ensure that the vehicle’s real driving route meets requirements with high stability control. The steering

Energies 2020, 13, 6659; doi:10.3390/en13246659 www.mdpi.com/journal/energies Energies 2020, 13, 6659 2 of 12 wheel angle is determined by the difference between vehicle lateral displacement and the target route, which needs to be accurately calculated and has a direct impact on vehicle tracking accuracy. The driver model proposed in the existing literature uses vehicle longitudinal displacement and the relation between longitudinal displacement and lateral displacement during the preview time to identify the position of the target point when calculating the lateral displacement difference [11]. The target point determined at the last moment cannot be reached due to the real-time change of steering wheel angle when turning the vehicle. Besides, the existing algorithms lack consideration regarding the influence of steering wheel angle on the vehicle driving stability when determining the steering wheel angle. Based on accurate prediction of the difference of vehicle lateral displacement, this article proposes a dual-objective optimized control strategy that considers vehicle tracking ability and driving stability and contains settable parameters according to the driver’s driving reaction, which differs due to individual driving skill level when the electronic control function fails. In the end, the effect of electronic control function failure and its ASIL can be concluded.

2. Driver Model Based on Multi-Objective Optimization Compared with the multi-point preview or interval preview method, there is no need to accumulate or integrate differences at multiple preview points within the preview time using the single-point preview method, which suggests a simple calculation. In addition, with a single-point preview method, only one point on the target route is used, which results in a better tracking ability under stable driving. Due to the lack of optimization on vehicle driving stability during the entire preview period, the single-point preview model proposed in the existing literature can hardly keep the vehicle in an optimized lateral adhesion condition, especially when the curvature is large and the adhesion is poor on the target route. In order to establish a simulation model with a small amount of calculation, accurate tracking ability, and prevention of vehicle instability due to incorrect steering wheel angle input, this article proposes an algorithm using the single-point preview method with consideration of vehicle lateral adhesion condition for determination of the steering wheel angle. In the proposed driver model, the steering wheel angle is optimized with consideration of both the vehicle lateral displacement difference and the lateral deviation of vehicle front and rear axles. It is divided into the following steps in detail: firstly, the target route in the preview interval is identified according to the planned driving route. Secondly, the steering angle is determined to minimize the difference between vehicle position and target route in both lateral and longitudinal direction, and to optimize vehicle steering characteristics.

2.1. Calculation of Steering Wheel Angle

2.1.1. Determination of Target Route In the vehicle coordinate system, the function of ﬁtting the horizontal coordinate of the target route to the vertical coordinate is the following:

n P i yp = fp xp = aixp . (1) i=0 where xp, yp are the x- and y-component of the vehicle route, respectively. When turning the vehicle, n 2, and the target route is a non-linear function. In this paper, considering that the driver only ≥ drives the vehicle along a parabolic trajectory during the short preview time, the target route is ﬁtted to a quadratic function as follows:

2 yp = a2xp + a1xp + a0. (2) EnergiesEnergies 20202020,, 1313,, 6659x FOR PEER REVIEW 33 of 1212

2.1.2. Determination of Lateral Displacement Difference 2.1.2. Determination of Lateral Displacement Diﬀerence To acquire the displacement in the current 𝑥𝑂𝑦 coordinate system after preview interval 𝑇, a simplifiedTo acquire 2-DOF the vehicle displacement model is in introduced the current in xOyFigurecoordinate 1 [12]. Symbolic system aftervariables preview 𝑣,𝑣 interval stand forT, athe simpliﬁed velocity 2-DOFat the vehiclefront and model rear iswheels, introduced respectively, in Figure while1[ 12]. 𝑙 Symbolicis the wheelbase; variables v𝐹1, ,𝐹v2stand are forthe thelateral velocity forces at theacted front on andthe rearfront wheels, and rear respectively, wheels, while𝛼,𝛼l isare the the wheelbase; slip angles,Fy1 , 𝑢Fy 2andare the𝑣 are lateral the forceslongitudinal acted on and the lateral front velocity and rear of wheels, the vehicle,α1, α respectively,2 are the slip angles,𝑎 and 𝛾u and are thev are lateral the longitudinal acceleration andand lateralyaw rate. velocity of the vehicle, respectively, ay and γ are the lateral acceleration and yaw rate.

FigureFigure 1.1. A 2-DOF vehicle model.

TheThe displacementdisplacement (x𝑥t,,𝑦yt) can can be be obtained obtained according according to to the the above above model, model, R h 1 1 i 𝑥 = 𝑢 Tcos 𝛾𝑡 + 𝛾𝑡−𝑣+𝑎1 . 2 𝑡 sin 𝛾𝑡 + 𝛾1𝑡.2 d𝑡 xt = u cos 2γt + γt v + ayt sin γt 2+ γt dt 0 2 − 2 . . (3) (3) R Th 1 1 . 2 1 1 . 2i 𝑦 = yt 𝑢= sinu sin𝛾𝑡 + γt𝛾+𝑡+𝑣+𝑎γt + v +𝑡ay cost cos 𝛾𝑡γt + +𝛾𝑡γt d𝑡dt 0 2 2 2 2 As sin 𝛾𝑡1 + . 𝛾2𝑡≅sin𝛾𝑡, cos 𝛾𝑡1 . + 2𝛾𝑡 ≅ cos𝛾𝑡, this can be solved, As sin γt + 2 γ t sin(γt), cos γt + 2 γt cos(γt), this can be solved, 𝑇 cos𝛾𝑇 sin𝛾𝑇 1 𝑥 ≅ T cos(+γT) sin(γ𝑎T) + 1[𝑢 sin𝛾𝑇 + 𝑣 cos𝛾𝑇 −𝑣] xt + ay + [u sin(γT) + v cos(γT) v] (4a)(4a) 𝛾 γ 𝛾 γ2 𝛾 γ − 𝑇sin𝛾𝑇 [1 − cos𝛾𝑇] 1 𝑦 ≅ T sin+(γT) [1 cos(γT)]𝑎 + 1[𝑢 − 𝑢 cos 𝛾𝑇 +𝑣sin𝛾𝑇]. yt + − ay + [u u cos(γT) + v sin(γT)]. (4b) (4b) 𝛾 γ 𝛾 γ2 𝛾γ −

Therefore,Therefore, the abscissa of the preview point y𝑦pt ==𝑓fp(𝑥xt). Further, Further, we we have have Δ𝑦∆y = =y 𝑦 pt−𝑦yt andand . − a𝑎y==𝑣v ++𝑢𝛾uγ.. AssumeAssume k𝑘f and andkr represent𝑘 represent the corneringthe cornering stiﬀ nessesstiffnesses of front of front and rearand axlesrear axles while whileIz is the 𝐼 momentis the moment of inertia of inertia about zaboutaxis, β𝑧 isaxis, the slip𝛽 is angle the slip of theangle mass of center.the mass Then, center. the Then, following the following equation isequation achieved: is achieved:   " . #  k f  k f +kr ak f bkr +  β + − γ  v uγ 𝑘  m 𝑘 +𝑘 m 𝑎𝑘 −𝑏𝑘mu  . =  − δ +  2 2  (5) ⎡ − ⎤ ak⎡f   ak𝛽+f bkr a k f +b𝛾 kr ⎤  γ    − β + γ  𝑣 +𝑢𝛾 𝑚 Iz 𝑚 Iz 𝑚𝑢 uIz =⎢ ⎥ 𝛿+− ⎢ ⎥ (5) 𝛾 𝑎𝑘 𝑎𝑘 −𝑏𝑘 𝑎 𝑘 +𝑏 𝑘 Thus, ⎢− ⎥ ⎢ 𝛽+ 𝛾⎥ ⎣ 𝐼 ⎦ ⎣ 𝐼2 𝑢𝐼 ⎦ ∆y = τ2δ + τ1δ + τ0. (6) Thus,

Δ𝑦 = 𝜏𝛿 +𝜏𝛿+𝜏. (6)

2.1.3. Constraints of Vehicle Steering Characteristics When determining the wheel angle, the balance between slip angles of the vehicle’s front and rear axles is considered in this paper. According to the kinematics relation in the 2-DOF model [13], the following equations can be obtained:

Energies 2020, 13, 6659 4 of 12

. . v+vT+a(γ+γT) α1 = u δ . . (7) v+vT b(γ+γT)− − α2 = u

When the two slip angles satisfy α α = 0, the vehicle is in neutral steering. Therefore, | 1 − 2| the following equation is introduced to characterize the influence of the steering wheel angle on the vehicle steering characteristics, ∆α = α α , (8) 1 − 2 which could be further written as: ∆α = σ1δ + σ0. (9) Equation (8) uses the difference between the front and rear axle tire sideslip angles to characterize the steering characteristics of the vehicle. Equation (7) describes that this difference is a linear function of the steering angle.

2.1.4. Optimized Control of Steering Wheel Angle It is assumed that when the driver is deciding the steering wheel angle, the lateral displacement diﬀerence between vehicle and preview point ∆y and the slip angle diﬀerence ∆α are both minimized. This could be abstracted into solving the following optimized problem [14]: 2 2 δopt = min J = ξy∆y + (ξα∆α) (10) δ where the objective function J could be written as:

4 3 2 J = ρ4δ + ρ3δ + ρ2δ + ρ1δ + ρ0, (11) and ξy, ξα represent the weight coefficient of lateral displacement difference ∆y and slip angle difference ∆α, respectively, when determining steering wheel angle.

2.2. Solution to the Problem This paper establishes a linear transferring relationship from steering wheel angle to vehicle lateral acceleration and yaw acceleration based on a simplified vehicle model. However, the target route in the vehicle coordinate system is a non-linear function, which leads to a nonlinear relationship between ∆y and wheel angle δ in the optimized objective function; the optimization objective is a high-order function of the wheel angle δ. A simplified solution that takes both calculation cost and accuracy of the result into account is then adopted. It is assumed that the velocity is constant during the preview interval, based on which the exact position of the preview point is obtained. Then, the objective function is simplified from a high-order function to a quadratic one that could be resolved for an initial optimized point δd. Assuming the vehicle is turning steadily with a constant velocity in preview interval T, and the position of the vehicle (xt0, yt0) is calculated after the preview period, when the wheel angle is modified from δ to δt, the lateral displacement difference is the following:

T2 0 ∆y = fp (xt ) yt a (12) 0 0 − 0 − 2 y Energies 2020, 13, 6659 5 of 12

0 where ay describes the variation in lateral acceleration generated after the steering wheel angle is 0 altered, relationships a δt and ∆y δt are then satisﬁed. The multi-objective optimization is y ∝ 0 ∝ transformed into quadratic convex optimization that could be expressed as,    " #T" #T" #" #  ∆y0 ξy 0 ξy 0 ∆y0  δopt = minJ0 = . (13) δ  ∆α 0 ξα 0 ξα ∆α 

To simplify it for a solution, the optimization is the following:

n T o δopt = min J0 = [G0δ + ∆c] [G0δ + ∆c] (14) δ " # " # G T2k (a+b)Tak ∆ where G = 110 in which G = f and G = f + 1 ξ , and ∆ = c11 in which, 0 110 2m 210 uIz α c G210 − ∆c21 T2 k f +kr ak f bkr ∆ = fp(xt ) yt β + − γ ξy (15) c11 0 − 0 − 2 m mu and, 2 2 (a+b)γξ (a+b)Tξ ak f bkr a k f +b kr ∆ = α + α − β + γ (16) c21 u u Iz uIz The solution to the optimization issue [15] could be obtained,

T 1 T δ = G G − G ∆c. (17) d − 0 0 0 2.3. Steering Wheel Angle Relevant to the Driver’s Response Lag After the optimum steering wheel angle is deﬁned, the driver controls the steering wheel to follow the target value. Taking into account the response lag of the human nervous system and inertial response lag, the lag processing step is added [16,17]. Finally, the relation of steering wheel angle δo and its theoretical optimum value δd is the following:

t s e− d δo = δ . (18) 1+ths d

In the lag processing step, 1 + ths represents the inertial response lag of the driver when controlling t s the steering wheel, and e− d characterizes the response lag of the human nervous system. In the low-frequency range, t s 1 tds/2 e− d = − , (19) 1+tds/2 where td is the lag time of the nervous system.

3. Model Simulation and Veriﬁcation

3.1. Model Overview The model for simulation in this article consists of models of a driver, electronic drive system, brake system, wheel, and body motion. It also diﬀers in terms of roads status with variable grades and adhesion coeﬃcients. The vehicle model has eight degrees of freedom [18]: lateral and longitudinal velocity, yaw velocity, revolving speed of four wheels and the wheel angle. The system layout is illustrated in Figure2. Energies 2020, 13, x FOR PEER REVIEW 5 of 12

𝛿 =min𝐽 = [𝐺 𝛿+∆] [𝐺 𝛿+∆] (14) 𝐺 Δ where 𝐺 = in which 𝐺 = and 𝐺 =− +1𝜉, and ∆= in which, 𝐺 Δ 𝑇 𝑘 +𝑘 𝑎𝑘 −𝑏𝑘 Δ = 𝑓 𝑥 −𝑦 − 𝛽+ 𝛾 𝜉 (15) 2 𝑚 𝑚𝑢 and, 𝑎+𝑏𝛾𝜉 𝑎+𝑏𝑇𝜉 𝑎𝑘 −𝑏𝑘 𝑎 𝑘 +𝑏 𝑘 Δ = + 𝛽+ 𝛾 (16) 𝑢 𝑢 𝐼 𝑢𝐼 The solution to the optimization issue [15] could be obtained,

𝛿 =−𝐺 𝐺 𝐺 ∆. (17)

2.3. Steering Wheel Angle Relevant to the Driver’s Response Lag After the optimum steering wheel angle is defined, the driver controls the steering wheel to follow the target value. Taking into account the response lag of the human nervous system and inertial response lag, the lag processing step is added [16,17]. Finally, the relation of steering wheel angle 𝛿 and its theoretical optimum value 𝛿 is the following: 𝑒 𝛿 = 𝛿. (18) 1+𝑡𝑠

In the lag processing step, 1+𝑡𝑠 represents the inertial response lag of the driver when controlling the steering wheel, and 𝑒 characterizes the response lag of the human nervous system. In the low-frequency range, 1−𝑡𝑠2⁄ 𝑒 = , (19) 1+𝑡𝑠2⁄ where 𝑡 is the lag time of the nervous system.

3. Model Simulation and Verification

3.1. Model Overview The model for simulation in this article consists of models of a driver, electronic drive system, brake system, wheel, and body motion. It also differs in terms of roads status with variable grades and adhesion coefficients. The vehicle model has eight degrees of freedom [18]: lateral and Energieslongitudinal2020, 13 velocity,, 6659 yaw velocity, revolving speed of four wheels and the wheel angle. The system6 of 12 layout is illustrated in Figure 2.

Destination

Steer Torque Steer System Model Steer Angle

Brake System Model Wheel Torque Vehicle Body, Wheels & Road Driver Model Drive System Model Model

Energies 2020, 13, x FOR PEER FigureREVIEW 2. Driver–vehicle–environment simulation model. 6 of 12

The roadroad withwith a a variable variable adhesion adhesion coe coefficientﬃcient could coul bed be used used to simulateto simulate the scenariothe scenario on a on rural a rural road thatroad isthat partly is coveredpartly covered with either with snow either or ice.snow In thisor ice. article, In this according article, to according the wheel’s to displacement, the wheel’s thedisplacement, contact torque the contact between torque the tire between and the the road tire surfaceand the in road the surface model reﬂectsin the model the impact reflects on the adhesion impact byon aadhesion partially by icy a roadpartially [19], icy as Figureroad [19],3 demonstrates. as Figure 3 demonstrates.

Figure 3. The road model with variable adhesion coecoefficient.ﬃcient.

3.2. Simulation Model Calibration and Verification Veriﬁcation To assureassure the model accuracy, real vehicle tests are conducted on on an an EV160 EV160 from from BAIC-EV. BAIC-EV. Model calibration and veriﬁcationverification are thenthen performedperformed accordingaccording toto thethe datadata collected.collected. The main parameters of the test vehicle cancan bebe foundfound inin TableTable1 1..

Table 1. Test vehicle parameters.

ItemItem SymbolSymbol Value Value WheelbaseWheelbase (mm) (mm) l l 2500 2500 Wheel Track (Front/Rear) (mm) Lf/Lr 1460/1445 Wheel Track (Front/Rear) (mm) L f / Lr 1460/1445 Approach/Departure Angle (◦) ϕf/ϕr 17/25 Curb weight (kg) m ϕ ϕ 1295 Approach/Departure Angle (°) f / r 17/25 Drive Motor Type - PMSM Rated Power/RevolvingCurb weight Speed/Torque (kg) (kW/rpm/Nm) Pr/nr/Tr m 30/2812/102 1295 Peak Power/RevolvingDrive SpeedMotor/Torque Type (kW/rpm/Nm) Pp/np/Tp - 53/9000/180 PMSM Reducer Gear Ratio - 7.793 Rated Power/Revolving Speed/Torque (kW/rpm/Nm) Pr / nr /Tr 30/2812/102

Peak Power/Revolving Speed/Torque (kW/rpm/Nm) Pp / np /Tp 53/9000/180 In order to complete the calibration and veriﬁcation, two testing conditions are conducted for Reducer Gear Ratio - 7.793 data collection. One is an acceleration and sliding experiment in a straight direction to validate the response characteristics of vehicle velocity with the input from the acceleration pedal. The other is the In order to complete the calibration and verification, two testing conditions are conducted for data collection. One is an acceleration and sliding experiment in a straight direction to validate the response characteristics of vehicle velocity with the input from the acceleration pedal. The other is the double-lane-change experiment that could verify the response characteristics of the vehicle’s steering status with the input from the steering wheel. In the straight driving test, the driver releases the brake pedal after the vehicle starts to run and then quickly steps on the acceleration pedal to speed up the vehicle to 100 km/h. The pedal is then released while the driver only gets control of the steering wheel to maintain straight direction until the velocity reduces to around 6 km/h when the experiment ends. Throughout the experiment, the output driving torque, the regenerative braking torque, and revolving speed are collected from the electric motor. The input, being transferred into the driver–vehicle–environment model, includes acceleration pedal position and driving torque. The results are shown in Figure 4–7.

Energies 2020, 13, 6659 7 of 12 double-lane-change experiment that could verify the response characteristics of the vehicle’s steering status with the input from the steering wheel. In the straight driving test, the driver releases the brake pedal after the vehicle starts to run and then quickly steps on the acceleration pedal to speed up the vehicle to 100 km/h. The pedal is then released while the driver only gets control of the steering wheel to maintain straight direction until the velocity reduces to around 6 km/h when the experiment ends. Throughout the experiment, the output driving torque, the regenerative braking torque, and revolving speed are collected from the electric motor. The input, being transferred into the driver–vehicle–environment model, includes acceleration pedalEnergiesEnergies position 20202020,, , 13 13 and, ,, x xx FOR FORFOR driving PEER PEERPEER REVIEW REVIEWREVIEW torque. The results are shown in Figures4–7. 77 ofof 1212 Energies 2020, 13, x FOR PEER REVIEW 7 of 12 200200 200

100100 100

00 00246810121402468101214 02468101214 Time/Time/ ss Time/ s FigureFigure 4.4. DriveDrive torquetorque underunder straightstraight driving.driving. FigureFigure 4. Drive4. Drive torque torque under under straight straight driving. driving.

50 5050

Motor Brake Torque/ Nm Torque/ Brake Motor 0 Motor Brake Torque/ Nm Torque/ Brake Motor 0 10203040 Motor Brake Torque/ Nm Torque/ Brake Motor 0 10203040

Motor Brake Torque/ Nm Torque/ Brake Motor 0 10203040 Time/Time/ ss Time/ s FigureFigure 5.5. RegenerativeRegenerative brakingbraking torquetorque underunder straightstraight driving.driving. FigureFigure 5. Regenerative5. Regenerative braking braking torque torque under under straight straight driving. driving. 150 150150 TestTest Test 100100 SimulationSimulation 100 Simulation 50 5050 00 00246810121402468101214 02468101214Time/ s Time/Time/ s s Time/ s FigureFigureFigure 6. 6.6.Speed SpeedSpeed comparison comparisoncomparison during duringduring acceleration: acceleration:acceleration: simulation simulationsimulation and andand real realreal test. test.test. Figure 6. Speed comparison during acceleration: simulation and real test. 100 100100 TestTest Test SimulationSimulation 50 Simulation 5050

00 00 10203040 00 10203040 10203040 Time/Time/ ss Time/ s FigureFigureFigure 7. 7.7.Speed SpeedSpeed comparison comparisoncomparison during duringduring sliding slidingsliding braking. braking.braking. Figure 7. Speed comparison during sliding braking. InIn thethe double-lane-changedouble-lane-change experiment,experiment, aa typicaltypical ararrangementrangement ofof thethe lanelane andand roadblocksroadblocks [20][20] isis In the double-lane-change experiment, a typical arrangement of the lane and roadblocks [20] is illustratedillustrated inin FigureFigure 88 wherewhere 𝑆𝑆 =15=15 m,𝑆m,𝑆 == 30 30 m,m, 𝑆 𝑆 =𝑆=𝑆 =25=25 m,𝑆m,𝑆 == 30 30 m,m, 𝐵 𝐵 =1.1𝐵+=1.1𝐵+ illustrated in Figure 8 where 𝑆 =15 m,𝑆 = 30 m, 𝑆 =𝑆 =25 m,𝑆 = 30 m, 𝐵 =1.1𝐵+ 0.25 m, 𝐵 = 1.2𝐵 + 0.25 m, 𝐵 = 1.3𝐵 + 0.25 m and 𝐵 stands for the width of the vehicle. The 0.25 m, 𝐵 = 1.2𝐵 + 0.25 m, 𝐵 = 1.3𝐵 + 0.25 m andand 𝐵 standsstands forfor thethe widthwidth ofof thethe vehicle.vehicle. TheThe 0.25 m, 𝐵 = 1.2𝐵 + 0.25 m, 𝐵 = 1.3𝐵 + 0.25 m and 𝐵 stands for the width of the vehicle. The resultsresults areare shownshown inin FiguresFigures 99 andand 10.10. results are shown in Figures 9 and 10.

Energies 2020, 13, 6659 8 of 12

In the double-lane-change experiment, a typical arrangement of the lane and roadblocks [20] is illustrated in Figure8 where S1 = 15 m, S2 = 30 m, S3 = S4 = 25 m, S5 = 30 m, B1 = 1.1B + 0.25 m, BEnergiesEnergies2 = 1.2 2020 2020B +, ,13 130.25, ,x x FOR FORm ,PEER PEERB3 = REVIEW REVIEW1.3B + 0.25 m and B stands for the width of the vehicle. The results88 of areof 1212 shownEnergies 2020 in Figures, 13, x FOR9 and PEER 10 REVIEW. 8 of 12

FigureFigure 8. 8. A A typical typical arrangement arrangement of of the the test. test. See See the the text text for for detail. detail. Figure 8. A typical arrangement of the test. See the text for detail. Figure 8. A typical arrangement of the test. See the text for detail. Steering Wheel Angle/ ° Angle/ Wheel Steering Steering Wheel Angle/ ° Angle/ Wheel Steering Steering Wheel Angle/ ° Angle/ Wheel Steering

Figure 9. The driver’s steering wheel angle input (versus time) under double-lane-change test. FigureFigure 9. 9.The The driver’s driver’s steering steering wheel wheel angle angle input input (versus (versus time) time) under under double-lane-change double-lane-change test. test. Figure 9. The driver’s steering wheel angle input (versus time) under double-lane-change test. Lateral Displacement/Lateral m Lateral Displacement/Lateral m Lateral Displacement/Lateral m

FigureFigureFigure 10.10. 10. VehicleVehicle Vehicle pathpath path comparisoncomparison comparison underunder under double-lane-change.double-lane-change. double-lane-change. Figure 10. Vehicle path comparison under double-lane-change. 4. Driver Model’s Application in Functional Safety Simulation 4.4. DriverDriver Model’sModel’s ApplicationApplication inin FunctionalFunctional SafetySafety SimulationSimulation 4. Driver Model’s Application in Functional Safety Simulation 4.1. Driver Model Calibration 4.1.4.1. DriverDriver ModelModel CalibrationCalibration 4.1. DriverThirty Model drivers Calibration with distinct genders and driving experiences were invited to conduct a Thirty drivers with distinct genders and driving experiences were invited to conduct a double- double-lane-changeThirty drivers with experiment distinct ongenders EV160. and During driving the experiences test, the driverwere invited was required to conduct to keepa double- the lane-changeThirty drivers experiment with distincton EV160. genders During and the driving test, the experiences driver wa weres required invited to to keep conduct the accelerator a double- acceleratorlane-change pedal experiment and the brake on EV160. pedal During uncontrolled the test, totrack the driver the target was trajectory required byto turningkeep the the accelerator steering lane-changepedal and the experiment brake pedal on uncontrolledEV160. During to thetrack test, the the target driver trajectory was required by turning to keep the steeringthe accelerator wheel, wheel,pedal andand the the state brake parameters pedal uncontrolled of each driver to track were recordedthe target during trajectory the driving by turning of the the vehicle steering including wheel, pedaland the and state the parametersbrake pedal of uncontrolled each driver towere track recorded the target during trajectory the driving by turning of the the vehicle steering including wheel, four-wheeland the state speed, parameters vehicle longitudinal of each driver acceleration, were recorded lateral during vehicle the speed, driving yaw rate,of the GPS vehicle vehicle including speed, andfour-wheel the state speed, parameters vehicle of longitudinal each driver wereacceleration, recorded lateral during vehicle the driving speed, of yaw the vehiclerate, GPS including vehicle steeringfour-wheel wheel speed, angle, vehicle vehicle longitudinal longitudinal displacement,acceleration, lateral lateral vehicle displacement. speed, Accordingyaw rate, toGPS Equation vehicle four-wheelspeed, steering speed, wheel vehicle angle, longitudinal vehicle longitudinal acceleration, displacement, lateral vehicle lateral speed, displacement. yaw rate, AccordingGPS vehicle to (17)speed, and steering collected wheel data, theangle, least vehicle square longitudinal method is used displacement, to obtain the lateral characteristic displacement. parameters According of each to speed,EquationEquation nsteering (17)(17) andwheeland collectedcollectedo angle, vehicle data,data, thethelongitudinal leastleast squaresquare displacement, methodmethod isis lateral usedused displacement.toto obtainobtain thethe Accordingcharacteristiccharacteristic to driver: ξy, ξα, T, th, td where n = 1, 2, ... , 30. In total, 30 sets of parameters can be obtained and each Equationparametersparameters (17) ofof eachandeach driver:collecteddriver:n 𝜉𝜉 data,,𝜉,𝜉,𝑇,𝑡,𝑇,𝑡 the,𝑡 ,𝑡least where wheresquare 𝑛𝑛 method = = 1,2, 1,2, …is … .,30 used.,30 InIn total,total, to obtain 3030 setssets oftheof parametersparameters characteristic cancan set of parameters is substituted into the driver model to characterize the driving performance in the parametersbe obtained of and each each driver: set of parame𝜉,𝜉,𝑇,𝑡ters,𝑡 is substituted where 𝑛 into = the 1,2, driver … .,30 In model total, to30 characterize sets of parameters the driving can actualbe obtained double-lane and each change set of conditions. parameters Figure is substituted 11 shows into the the driving driver data model of 30 to drivers characterize and the the driving driving beperformance obtained and in eachthe actual set of paramedouble-laneters is change substituted cond intoitions. the Figuredriver model11 shows to characterize the driving the data driving of 30 trajectoryperformance of one in “virtualthe actual driver”. double-lane change conditions. Figure 11 shows the driving data of 30 performancedriversdrivers andand the thein drivingthedriving actual trajectorytrajectory double-lane ofof oneone change “virtual“virtual cond driver”.driver”.itions. Figure 11 shows the driving data of 30 drivers and the driving trajectory of one “virtual driver”.

Energies 2020, 13, 6659 9 of 12 EnergiesEnergies 2020 2020, ,13 13, ,x x FOR FOR PEER PEER REVIEW REVIEW 99 ofof 1212

FigureFigureFigure 11. 11.11. Vehicle Vehicle path pathpath of ofof 30 30+130+1+1 didifferentdifferentﬀerent drivers driversdrivers under underunder double-lane-change double-lane-changedouble-lane-change test. test.test.

4.2.4.2.4.2. FunctionalFunctional SafetySafety SimulationSimulation withwithwith thethethe New NewNew Driver DriverDriver Model ModelModel DuringDuringDuring the thethe functional functionalfunctional safety safetysafety design designdesign for the forfor regenerative thethe regenerativeregenerative braking controlbrakingbraking system controlcontrol [21 system–system23], simulation [21–23],[21–23], issimulationsimulation necessary is tois necessary performnecessary to toto acquire performperform the to severity,to acquireacquire controllability, thethe severity,severity, and controllability,controllability, fault tolerance andand time faultfault under tolerancetolerance the failure timetime modeunderunder of thethe “unexpected failurefailure modemode peak ofof “unexpected“unexpected regenerative peak brakingpeak regenerativeregenerative torque”. brakingbraking torque”.torque”. 4.2.1. Scenario Setting 4.2.1.4.2.1. ScenarioScenario SettingSetting This paper chooses the scenario with higher exposure rate to simulate the failure response, ThisThis paperpaper chooseschooses thethe scenarioscenario withwith higherhigher exexposureposure raterate toto simulatesimulate thethe failurefailure response,response, which is changing lanes with low speed on the slippery urban road under the condition of clear whichwhich isis changingchanging laneslanes withwith lowlow speedspeed onon thethe slippeslipperyry urbanurban roadroad underunder thethe conditioncondition ofof clearclear day.day. day. According to the external characteristics of the PMSM motor, in this low-speed scenario the AccordingAccording toto thethe externalexternal characteristicscharacteristics ofof ththee PMSMPMSM motor,motor, inin thisthis low-speedlow-speed scenarioscenario thethe regenerative braking torque can reach a peak, which is also a scenario when the risk of vehicle collision regenerativeregenerative brakingbraking torquetorque cancan reachreach aa peak,peak, whichwhich isis alsoalso aa scenarioscenario whenwhen thethe riskrisk ofof vehiclevehicle is higher than high-speed driving. As vehicle A runs on a wet urban road with an initial velocity of collisioncollision isis higherhigher thanthan high-speedhigh-speed driving.driving. AsAs vevehiclehicle AA runsruns onon aa wetwet urbanurban roadroad withwith anan initialinitial 30 km/h, the driver starts the double-lane change to avoid vehicle B [24] as well as vehicle C in the velocityvelocity ofof 3030 km/h,km/h, thethe driverdriver starstartsts thethe double-lanedouble-lane changechange toto avoidavoid vehiclevehicle BB [24][24] asas wellwell asas vehiclevehicle opposite lane. At this time, the maximum regenerative braking torque appears, causing the front axle CC inin thethe oppositeopposite lane.lane. AtAt thisthis time,time, thethe maximummaximum regenerativeregenerative brakingbraking torquetorque appears,appears, causingcausing thethe of the vehicle to lock, and the steering is out of control, which may lead to a crash. The scenario is frontfront axleaxle ofof thethe vehiclevehicle toto lock,lock, andand thethe steeringsteering isis outout ofof control,control, whichwhich maymay leadlead toto aa crash.crash. TheThe shown in Figure 12. scenarioscenario isis shownshown inin FigureFigure 12.12.

Figure 12. A typical double-lane-change scenario for functional safety simulation. FigureFigure 12.12. AA typicaltypical double-lane-changedouble-lane-change scenarioscenario forfor functionalfunctional safetysafety simulation.simulation. 4.2.2. Simulation Result 4.2.2.4.2.2. SimulationSimulation ResultResult The results demonstrated in Figures 13 and 14 show that when the peak regenerative braking The results demonstrated in Figures 13 and 14 show that when the peak regenerative braking torqueThe was results applied demonstrated to the front in axle, Figures the driver 13 and lost 14 vehicleshow that control when and the the peak controllability regenerative wasbraking C3, torque was applied to the front axle, the driver lost vehicle control and the controllability was C3, whichtorque is was a level applied in ISO26262 to the front described axle, the as “uncontrollabledriver lost vehicle condition”. control and Figure the controllability15 gives the reason was C3, of which is a level in ISO26262 described as “uncontrollable condition”. Figure 15 gives the reason of reversewhich is yaw a level shown in ISO26262 in Figure described13. At this as time, “uncontrollable due to the lateralcondition”. instability Figure of 15 the gives vehicle, the reason the lane of reverse yaw shown in Figure 13. At this time, due to the lateral instability of the vehicle, the lane changereverse was yaw not shown completed in Figure in time 13. which At this led time, to collision due to with the vehiclelateral instability B in the current of the lane. vehicle, Thecollision the lane change was not completed in time which led to collision with vehicle B in the current lane. The speedchange was was 24.9 not km completed/h, so the severity in time is which S2 according led to toco ISO26262.llision with Together vehicle withB in thethe wet current road exposurelane. The collision speed was 24.9 km/h, so the severity is S2 according to ISO26262. Together with the wet road ratecollision E3, the speed functional was 24.9 safety km/h, level so ofthe the severity regenerative is S2 according braking control to ISO26262. system Together is ASIL B with according the wet to road the exposure rate E3, the functional safety level of the regenerative braking control system is ASIL B calculationexposure rate method E3, the of ASIL functional in ISO26262. safety Basedlevel of on the this, regenerative the safety goal braking is to “avoidcontrolpeak system regenerative is ASIL B according to the calculation method of ASIL in ISO26262. Based on this, the safety goal is to “avoid brakingaccording torque to the during calculation driving, method which of causes ASIL wheels in ISO26262. locking Based and sideslip”. on this, the The safety corresponding goal is to “avoid safety peak regenerative braking torque during driving, which causes wheels locking and sideslip”. The statuspeak isregenerative “the regenerative braking braking torque torqueduring output driving, by which the drive causes motor wheels is zero”. locking and sideslip”. The corresponding safety status is “the regenerative braking torque output by the drive motor is zero”. correspondingAs shown in safety Figures status 16–18 is, “the it could regenerative be obtained br fromaking the torque result output that when by the maximumdrive motor application is zero”. As shown in Figures 16–18, it could be obtained from the result that when the maximum time ofAs unexpected shown in peakFigures torque 16–18, is 300 it ms,could the be driver obtained is capable from ofthe controlling result that the when vehicle the to maximum complete application time of unexpected peak torque is 300 ms, the driver is capable of controlling the vehicle theapplication double-lane time change. of unexpected Therefore, peak the torque fault toleranceis 300 ms, time the intervaldriver is iscapable determined of controlling as 300 ms. the vehicle toto completecomplete thethe double-lanedouble-lane change.change. Therefore,Therefore, thethe faultfault tolerancetolerance timetime intervalinterval isis determineddetermined asas 300300 ms.ms.

Energies 2020, 13, x FOR PEER REVIEW 10 of 12

Energies 2020, 13, 5x FOR PEER REVIEW 10 of 12 Energies 2020, 13, x FOR PEER REVIEW 10 of 12 Energies 2020, 135, 66590 Obstacle 10 of 12

5 Reverse Yaw Obstacle 0 -5 Crash!

5 0 60 Reverse Yaw80 Obstacle100 120 140 160 -5 Crash! LateralDisplacement/ m 0 Reverse Yaw LongitudinalObstacle Displacement/ m -560 80 Crash!100 120 140 160 Reverse Yaw LateralDisplacement/ m Longitudinal Displacement/ m -560 80 Crash!100 120 140 160 Figure 13. Vehicle path in a failure scenario. LateralDisplacement/ m 60 80 Longitudinal100 Displacement/120 m 140 160

LateralDisplacement/ m Figure 13. VehicleLongitudinal path inDisplacement/ a failure scenario. m

FigureFigure 13. 13.Vehicle Vehicle path path in in a a failure failure scenario. scenario. Figure 13. Vehicle path in a failure scenario.

Figure 14. Steering wheel angle input (from the driver).

2 FigureFigure 14. 14.Steering Steering wheel wheel angle angle input input (from (from the the driver). driver). Figure 14. Steering wheel angle input (from the driver). Yaw 2 Moment 0 Yaw 2 Moment 0

2 Yaw -2 Moment 0 70 72 74 76 78 80

LateralDisplacement/ m Yaw -2 LongitudinalMoment Displacement/ m 70 0 72 74 76 78 80

LateralDisplacement/ m -2 Longitudinal Displacement/ m 70 72 Figure 15.74 Reverse yaw fo76rce analysis. 78 80

LateralDisplacement/ m -2 70 72FigureLongitudinal 15. Reverse74 Displacement/ yaw force analysis. 76m 78 80

LateralDisplacement/ m Figure 15.Longitudinal Reverse yaw Displacement/ force analysis. m Figure 15. Reverse yaw force analysis. 6 Figure 15. Reverse yaw force analysis. 300ms with wrong 4 Torque 6 2 300ms with wrong 4 6 0 350ms with wrong Torque 2 Torque 300ms with wrong 4 -26 Torque 0 60 80 350ms100 with wrong 120 140300ms with wrong160 LateralDisplacement/2 m 4 Torque Torque -2 350msLongitudinal with wrong Displacement/ m 0602 80 100 120 140 160 Energies 2020LateralDisplacement/ m , 13, x FOR PEER REVIEW Torque 11 of 12 Figure 16. FTT calculation350ms by with fault wrong injection simulation. -2 0 Longitudinal Displacement/ m 60 Figure80 16. FTT 100calculationTorque by fault120 injection simulation.140 160 LateralDisplacement/ m -2 60 80 Longitudinal100 Displacement/120 m 140 160 LateralDisplacement/ m Figure 16. FTT calculation by fault injection simulation. Longitudinal Displacement/ m Figure 16. FTT calculation by fault injection simulation. Figure 16. FTT calculation by fault injection simulation.

FigureFigure 17. 17.Steering Steering wheel wheel angle angle (versus (versus time) time) by by the the driver. driver.

Figure 18. Steering torque input (versus time) by the driver.

5. Conclusions This paper proposes a new design of driver model based on multi-objective optimization, and functional safety simulation is carried out with it. Conclusions can be drawn as follows: (1) Steering wheel angle in preview interval is calculated based on deviation of sideslip angle between front and rear axle and minimizing lateral displacement difference. After steering wheel angle is obtained, drivers with different driving skills are simulated with definition of weight parameters in objective function of the multi-objective optimization. (2) A “driver-vehicle-environment” model is established. Simulation of a failed electronic control system is performed under the operation of different “drivers”, which helps eliminate the risk of accidents and is thus suitable for ASIL of an electronic control system. (3) After the simulation analysis, the functional safety goal is clearly defined for EV160 regenerative braking system under the condition of regenerative braking torque being out of control. The functional safety goal is to “avoid peak regenerative braking torque during driving, which causes wheels locking and sideslip. With ASIL B the fault tolerance time is 300 ms”.

Author Contributions: Formal analysis, X.Z.; Investigation, Z.Z.; Methodology, Y.Z.; Project administration, X.Z.; Visualization, H.W. All authors have read and agreed to the published version of the manuscript.

Funding: This work was supported in part by the National Natural Science Foundation of China under Grant 51775039, Grant 51861135301, and Grant 51805030; and in part by the Special Program for Science and Technology Funding for Innovative Talents under Grant 3052019009.

Acknowledgments: The authors would like to thank the reviewers for their corrections and helpful suggestions.

Conflicts of Interest: The authors declare no conflict of interest.

References

1. Tang, M. Application Status and Development Trend of Electronic Technology in Automobile. DEStech Trans. Eng. Technol. Res. 2016, 180–184, doi:10.12783/dtetr/mcee2016/6404. 2. Qin, R.; Xiaodong, W.; Min, X. Functional safety concept design for steer-by-wire system of road vehicle based on the ISO. J. Automot. Saf. Energy 2018, 9, 250–257. 3. Cheon, J.S.; Kim, J.; Jeon, J.; Lee, S.M. Brake by Wire Functional Safety Concept Design for ISO/DIS 26262. In SAE Technical Paper; SAE International: Warrendale, PA, USA, 2011.

Energies 2020, 13, x FOR PEER REVIEW 11 of 12

Energies 2020, 13, 6659 11 of 12 Figure 17. Steering wheel angle (versus time) by the driver.

FigureFigure 18. 18.Steering Steering torquetorque inputinput (versus(versus time) time) by by the the driver. driver.

5.5. ConclusionsConclusions ThisThis paperpaper proposes a a new new design design of of driver driver mo modeldel based based on onmulti-objective multi-objective optimization, optimization, and andfunctional functional safety safety simulation simulation is carried is carried out outwith with it. Conclusions it. Conclusions can canbe drawn be drawn as follows: as follows:

(1)(1) SteeringSteering wheelwheel angle angle in previewin preview interval interval is calculated is calculated based based on deviation on deviat of sideslipion of anglesideslip between angle frontbetween and rearfront axle and and rear minimizing axle and lateralminimizing displacement lateral displacement difference. After difference. steering wheelAfter anglesteering is obtained,wheel angle drivers is obtained, with diff erentdrivers driving with skillsdifferent are simulateddriving skills with are definition simulated of weight with definition parameters of inweight objective parameters function in of objective the multi-objective function of optimization.the multi-objective optimization. (2)(2) AA “driver-vehicle-environment”“driver-vehicle-environment” modelmodel isis established.established. SimulationSimulation ofof aa failedfailed electronicelectronic controlcontrol systemsystem isis performedperformed under under the the operation operation of of di difffferenterent “drivers”, “drivers”, which which helps helps eliminate eliminate the the risk risk of accidentsof accidents and and is thus is thus suitable suitable for for ASIL ASIL of anof electronican electronic control control system. system. (3)(3) AfterAfter thethe simulationsimulation analysis,analysis, thethe functionalfunctional safetysafetygoal goal isis clearlyclearly defineddefinedfor for EV160EV160 regenerativeregenerative brakingbraking system under under the the condition condition of of regenerative regenerative braking braking torque torque being being out outof control. of control. The Thefunctional functional safety safety goal goalis to is“avoid to “avoid peak peakregenerative regenerative braking braking torque torque during during driving, driving, which whichcauses causes wheels wheels locking locking and sideslip. and sideslip. With ASIL With B ASIL the fault B the tolerance fault tolerance time is time 300 isms”. 300 ms”. Author Contributions: Formal analysis, X.Z.; Investigation, Z.Z.; Methodology, Y.Z.; Project administration, AuthorX.Z.; Visualization, Contributions: H.W.Formal All author analysis,s have X.Z.; read Investigation, and agreed Z.Z.; to the Methodology, published version Y.Z.; Project of the administration,manuscript. Z.X.; Visualization, H.W. All authors have read and agreed to the published version of the manuscript. Funding: This work was supported in part by the National Natural Science Foundation of China under Grant Funding:51775039,This Grant work 51861135301, was supported and inGrant part by51805030; the National and Naturalin part Scienceby the FoundationSpecial Program of China for underScience Grant and 51775039,Technology Grant Funding 51861135301, for Innovati and Grantve Talents 51805030; under and Grant in part 3052019009. by the Special Program for Science and Technology Funding for Innovative Talents under Grant 3052019009. Acknowledgments:Acknowledgments:The The authors authors would would likelike toto thankthank thethe reviewersreviewers forfor theirtheir correctionscorrections andand helpfulhelpful suggestions.suggestions. ConflictsConflicts of of Interest: Interest:The The authors authors declare declare no no conflict conflict of of interest. interest.

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