Multi-performance Target Collaborative Optimization Methods for Battery Electric Vehicle

: The present studies on battery electric vehicles (BEVs) has mainly focused on the single-objective 4 or weighted multi-objective optimization based on energy management, which can not manifest the coupling 5 relationship among the vehicle performance objectives essentially. To optimize the handling stability, ride comfort 6 and economy of BEV, this paper built the stability dynamics analysis model, ride comfort simulation half-car 7 model and power consumption calculation model of BEV, as well as two-point virtual random excitation model on 8 Level B road and proposed related evaluation indexes, including vehicle handling stability factor, weighted 9 acceleration root-mean-square (RMS) value of vertical vibration at the driver’s seat and power consumption per 10 100 m at a constant speed. The Pareto optimum principle – based multi-objective evolutionary algorithm (MOEA) 11 of BEV was also designed, which was encoded with real numbers and obtained the target values of all optional 12 schemes via MATLAB/Simulink simulation software. The merits and demerits of alternative schemes could be 13 judged according to the Pareto dominance principle, so that alternative schemes obtained after optimization were 14 realizable. The results of simulation experiment suggest that the proposed algorithm can perform the 15 multi-objective optimization on BEV, and obtain a group of Pareto optimum solutions featured by high handling 16 stability, favorable ride comfort and low energy consumption for the decision-makers. 17


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The efficient operation of BEV entails the coordination of handling stability, ride comfort and economy, with 23 non-differentiable, discontinuous, hybrid, multidimensional, constrained and nonlinear characteristics in its mocel, 24 which is a typical hybrid nonlinear multi-objective optimization issue. Els et al. optimized the suspension 25 characteristic parameters with dynamic-Q algorithm, for the multi-objective optimization of vehicle handling 26 stability and ride comfort, and provided a set of suspension parameters which can improve vehicle handling 27 stability and ride comfort for decision makers [1] . Yang Guangci et al. optimized the fuel consumption, HC+NOx 28 emissions and CO emissions of hybrid electric vehicle (HEV), and proposed a multi-objective optimization 29 evolutionary algorithm based on the Pareto optimum principle for HEV, thus obtaining the Pareto optimum 30 solution set with low fuel consumption and low emissions [2] . Zhang Jingmei et al. improved the genetic algorithm 31 to realize the multi-objective comprehensive optimization of ride comfort, handling stability and road-friendliness 32 of vehicles, and obtained the best matching value of suspension stiffness and damping [3] . Yang Rongshan et al. and Pareto frontier were obtained [6] . Chen Yikai et al. determined the optimum control parameters to make road 41 friendliness and ride comfort of vehicles comprehensively through range and variance analysis, in order to 42 improve road friendliness and ride comfort of vehicles at the same time. The simulation results show that the grade [7] . Zhang Zhifei et al. took the vertical acceleration of the driver and the frame and the sum of the 95th 45 percentile to the fourth power as the performance optimization indexes, to normalize the weight of indexes to a 46 single-objective function by analytic hierarchy process for improving ride comfort and road friendliness of 47 commercial vehicles, as well as optimizing the stiffness and damping of suspension by genetic algorithm. The 48 simulation results show that ride comfort and road friendliness of optimized vehicles are improved effectively [8] . 49 Yang Kun et al. conducted parameter sensitivity analysis on ride comfort and road friendliness of six-axle 50 semitrailer with the optimal Latin hypercube experimental design method, selected appropriate parameters 51 combined with the actual situation and optimized ride comfort, road friendliness, the comprehensive performance 52 of ride comfort and road friendliness with neighborhood cultivated multi-objective genetic optimization 53 algorithm. The research results show that under the common driving speed, the evaluation indexes of selected 54 optimization scheme, smoothness and road friendliness can also be better optimized [9] . Zhou Feikun et al. carried 55 out multi-objective optimization on parameter matching of dynamical system with the optimization method of 56 SAPSO with average mileage under multiple working conditions, average total energy consumption under 57 multiple working conditions and complete vehicle kerb mass as the specific targets. The simulation results show 58 that the weight of vehicles can be reduced and the economic performance on the premise of ensuring the dynamic 59 performance can be improved [10] . Zhang Kangkang et al. compared and selected the 3 dynamical system 60 matching projects with maximum speed, acceleration time and power consumption per 100 km as the specific 61 targets, solved the problem of conflicting among indexes to be optimized with the multi-objective genetic 62 algorithm, described the competitive relationship between indexes with the Pareto matrix, and clearly defined the 63 constraints and scope of application of policies [11] . 64 through weighting or other methods, and then obtained the solution through mathematical programming. 66 preference knowledge (i.e. weight coefficient of each target), to build single-objective evaluation function; (2) A 68 majority of single-objective optimization technologies were based on local optimization search algorithm. Vehicles receive inputs from longitudinal, vertical, and transverse directions, from which, the motion 96 response characteristics are definitely interactive and coupled mutually. The influence of vertical coupling motion 97 generated by the listing under the working condition of uniform turning movement on the vertical comfort of the 98 driver can be ignored. Therefore, this paper considered the vertical motion of vehicles alone when building ride 99 comfort model. First of all, the complex vehicle system was properly simplified and assumed: 100 1) Vehicles are symmetrical to the longitudinal symmetry plane and road unevenness corresponding to the 101 four tires is the same; 2) It is assumed that the road unevenness conforms to the normal distribution of each state 102 after a stationary random process, the road unevenness corresponding to each tire on the same side is different, 103 with a response time delay caused by the wheelbase; 3) Both the stiffness of tires and seats are simplified into 104 linear function; Suspension damping is a linear function of speed; 4) Each tire has a single contact with the 105 ground , without any bounce; Road excitation acts on the central point of contact between tires and the road 106 After linearizing the automobile system into a half simplified model approximately, front and rear tires will 108 bear 2 random inputs, and the free-body diagram is shown as Figure 1. All parameters in Figure 1 6×6 is the response coefficient matrix of each response frequency. It has been verified that its rank is 128 Supposed that vehicle vertical displacement and lateral displacement are all zero, the systematic differential 148 equation of motion can be expressed as below by ignoring the influence of suspension temporarily under the input 149 of front wheel, and considering the planar motion of vehicle alone. 150 When the vehicle is moving at a constant circular motion type, ̇= 0 and ̇= 0, and the vehicle steering 153 sensitivity, = / , can be obtained. 1 and 2 are the cornering stiffness of front and rear tires, respectively. 154 According to Formula (3) and Formula (4), stability factor can be expressed as: 155 The tire cornering stiffness is closely related to the tire vertical load, which can be expressed as: 157 Where, ′ ( ) is the tire load of front and rear axles, respectively. and mean the left side and the right 159 Where, ( ) is the vertical reaction force of ground of front and rear axles and left (right) tire under an 162 idle status. The amount of change of vertical load includes two parts: , i.e., the dynamic load applied to front 163 and rear axles respectively by road random excitation and ∆ ( ) , the amount of change of vertical reaction 164 applied to front and rear axles and left (right) tire by the centrifugal force. Therefore, the improved stability factor 165 can be expressed as: 166 The road excitation born by vehicles in driving belongs to multiple-support excitation. In consideration of the 169 large wheel base, front and rear tires have receive stable and hysteresis road excitation of different phrases. A road 170 model is built within the frequency domain by taking Level B road surface as an example [14] . Suppose that front 171 and rear tires receive the same related stable road excitation, the two excitation points of road surface can be 172 expressed as: 173 ( ) can be regarded as the generalized single point excitation. Suppose that the auto-spectral density of ( ) 175 is a known constant, and the exciting moment born by front and rear tires is 1 and 2 , respectively, the 176 two-point virtual excitation model obtained with pseudo excitation method can be expressed as: 177 Where, ̃ and ̃ are virtual excitations born by front and rear tires, respectively. 179

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Handling stability of vehicles covers a broad range, which is mainly manifested by the time-frequency 182 response characteristics of vehicles in curve driving. When a vehicle turns a corner at a constant speed, the ratio of 183 yaw velocity to the turning angle of front wheel at a stable state is used as the response evaluation standard. 184 Differently, the value of stable state factor manifests the stable response of vehicles. Generally speaking, the 185 influence of vehicle structure parameters is considered only in the research analysis of stable state response of 186 vehicle when turning a corner. Hence, the influence of dynamic load caused by road random excitation and 187 suspension stiffness and damping and obtaining the improved stability factor was introduced in this paper, so that 188 the research of vehicle stability can be more accurate. The improved stability factor ( ) in Formula (8) was 189 taken as the evaluation index of listing handling stability here in this paper. 190

Evaluation Index of Economy
Where, = 100 , is listing resistance coefficient, is air resistance coefficient, is windward 206 area, is vehicle driving speed, is the efficiency of motor and controller, is the total efficiency of 207 drive system and is the average discharging efficiency of accumulator.

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The driving conditions set for optimization play a key role, for the speed and road conditions of the vehicle 223 always change in driving. According to the driving conditions set in this paper, the vehicle can be driven stably at 224 a constant speed (30 km/h) along Level B curved road with a 50 m turning radius. Generally speaking, vehicle 225 vibration becomes the most obvious and even resonance may be produced when excitation frequency is 3.15 Hz. 226 In other words, the vehicle's ride comfort and handling stability become the most sensitive. Therefore, the analysis 227 on multi-performance optimization was optimized at a road excitation frequency of 3.15 Hz [12] . 228 This paper took function ̈ (acceleration RMS value ̈ of the vertical vibration at the driver's seat), 229 (power consumption per 100 km at a constant speed) and handling stability factor K l(r) >0, which mean 12 reducing the acceleration RMS value of the vertical vibration at the driver's seat and power consumption per 100 231 km at a constant speed and making the vehicle lack of turning characteristics properly, as the optimization 232 objectives to meet the requirements of handling stability and ride comfort, and minimize power consumption as 233 much as possible. Set the following functions: 234 Where, is decision variables (or parameters to be optimized), decision variables and corresponding 236 constraint conditions, all of which vary along with specific optimized objects. 237

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The parameters which exert significant influence on the optimization objectives were optimized in this paper.  Table 1. 248   EV-MOEA has an evolution population, and each candidate solution is expressed by real number encoding. 280 The main procedures of the algorithm are shown in Figure 3. 281 [ , ](i=1,2,…m) (where, and mean lower limit and upper limit of , respectively). For the engineering 289 application, the precision that can be realized by each parameter of BEV is limited certainly, which is significant 290 only when the value of decision variables is within the range of realizable precision. The significant digit of 291 variables in this paper is set according to precision limitation and maximum generation, with the maximum 292 evolutionary algebra as the condition for judging the completion of evolutionary process. Therefore, the 293 evolutionary algebraic counter needs to be set and initialize into = 0. 294 Step (6), assign a value large enough to 1 ( ), 2 ( ) and 3 ( ), respectively, which means 323 that due to its unsuitable handling stability, poor ride comfort and economy, this solution is not directly eliminated 324 for storing diverse genes for subsequent evolutions.  Table 3. 331

Optimization Results and Analysis
efficiency of motor be and the efficiency of drive system be . The statistical results of the stability factor 336 1 corresponding to the final Pareto optimum solutions, the root mean square value of vertical vibration 337 acceleration at driver's seat, the power consumption per 100 km at a constant speed and system performance are 338 shown in Table 5. The data in Group 0 in Table 4 and Table 5   It can be found from the data in Table 5 that the optimized system has reduced the acceleration RMS value of 348 vertical vibration at driver's seat and the power consumption per 100 km at a constant speed under the premise of 349 guaranteeing vehicle handling stability. In the optimized system, stability factors have increased by 9.5%, the 350 acceleration RMS value of vertical vibration at driver's seat has decreased by 5.1% and the power consumption 351 per 100 km at a constant speed has decreased by 8.8% on average, respectively. 352 As for the efficiency of the system, the efficiency of motor and driving system has increased by 6.1% and 3.8% 353 on average, respectively, which implies that the working efficiency of major components of the vehicle has 354 increased after optimization and each subsystem has better matched, so the multi-performance optimization 355 proposed in this paper can improve the total working efficiency of BEVs. 356 As an example, the optimization solution of Group 1 was compared with the system before optimization. 357 According to Figure 6, the efficiency of driving system was within [0.8, 0.9] approximately before 372 optimization but mainly within [0.85, 0.95] after optimization, which shows that the efficiency of driving system 373 after optimization is superior to that before optimization, which is helpful to improve the comprehensive 374 efficiency of BEVs. handling stability. According to the simulation experiment, the algorithm has optimized multi-performance target 384 collaboratively such as the safety, comfort and energy conservation of BEVs. 385 (2) The working efficiency of motor and driving system of BEVs have been improved differently after 386 optimization, which means that each subsystem has been better matched after optimization and BEVs show a 387 better performance. 388 (3) The method proposed in this paper makes it unnecessary to simplify the multi optimization objectives 389 into one, which avoids the adverse influence caused by the weighted sum of different objectives, providing many 390 groups of optimum solutions.