Multi-objective optimum design of two-motor and two-speed powertrain system for electric vehicles with probabilistic driver model

Abstract

Because of the growing worldwide demand for solutions to environmental issues, a major trend observed in the automotive industry has been the change from the internal combustion engine vehicle (ICEV) to the electric vehicle (EV). As the powertrain system constitutes the main configuration difference between an ICEV and EV, it should be carefully designed. In particular, a two-motor and two-speed powertrain system can outperform other powertrain systems in terms of driving requirements, achieving a high dynamic performance and energy efficiency. The key design components of the powertrain system are the motor and transmission; hence, the specifications of these components should be optimized, to improve both performance and efficiency as much as possible. To analyze such requirements, an EV dynamic model, which includes a two-motor and two-speed powertrain system, was developed using a model-based design methodology. This model consists of driver, powertrain, equivalent vehicle inertia, resistance torque, braking, and battery sub-models. In real-world situations, variations in driver behavior can cause a variation in energy consumption under the same driving conditions. Therefore, an effective driver model, which precisely reflects the driver characteristics, is required to investigate the variation in driver behavior. For realizing this objective, this thesis has employed a driver model that expresses driver behavior using three parameters for the human operator: the aggressivity of driving, the perception of the driver, and the inherent viscosity and inertia of the driver’s muscles. Using a probabilistic approach, these parameters were described by probability density functions. The design parameters for the motors and transmission were defined as the maximum torque of each motor, the torque distribution coefficients between the two motors, and the first and second gear ratios of the transmission. To quantify the performance and efficiency, acceleration time and energy consumption were used as the evaluation criterion, respectively. The results obtained by changing the values of the design parameters show that the specifications of these parameters significantly affect the performance and efficiency of the EV. Therefore, optimizing these parameters is necessary to determine an effective design for the EV powertrain system. Moreover, because of a trade-off between performance and efficiency, a multi-objective optimization method is superior to a single-objective optimization method, for suggesting a variety of design solutions. Accordingly, this thesis formulates a multi-objective optimization problem that minimizes the acceleration time and energy consumption, and that includes dynamic constraints. Because of the large computational effort required to solve the multi-objective optimization problem using the analysis results of the EV model considering the probabilistic driver model, the surrogate models of each objective function were constructed, using an artificial neural network to reduce the computational burden. In addition, by employing an adaptive sampling method, the surrogate models were able to meet the high accuracy requirements of the models, using only a small number of samples to do so. Based on these surrogate models, the multi-objective optimization was performed, and the optimization results provided a Pareto front showing a variety of optimal design solutions that consider both objective functions simultaneously. Through a comparison with the results of a reference design, the superiority of the proposed design was confirmed. Moreover, by comparing the results of the optimal design solutions under both deterministic and probabilistic driver models, the necessity of the probabilistic model was made clear. Finally, comparisons of cost and accuracy between the EV dynamic model and the surrogate model verify the effectiveness of surrogate-based multi-objective optimization.|환경오염 문제에 대한 전 세계적인 관심이 증가됨에 따라 자동차 산업에서 이에 대한 해결책이 요구되고 있다. 이러한 이유로 최근 자동차 산업의 주요 개발 방향은 내연기관차(ICEV)에서 전기차(EV)로 급속히 변화하고 있다. ICEV와 EV의 가장 큰 차이점은 파워트레인 시스템이므로 해당 시스템의 설계는 EV개발 시 가장 고려되어야 할 부분이다. 특히 2모터 2단변속 파워트레인 시스템은 다른 EV 파워트레인 시스템 대비 우수한 동적성능과 에너지효율을 달성할 수 있다. 해당 시스템에서 핵심 설계 구성품은 모터와 변속기이기 때문에 이들 구성품의 설계사양은 성능과 효율을 최대한 향상시킬 수 있도록 최적화 되어야 한다. 차량 성능과 효율 분석을 위해 모델기반 설계 방법론을 활용하여 2모터 2단변속 파워트레인 시스템을 포함한 EV 동적 모델을 개발하였다. 해당 모델은 운전자, 파워트레인, 등가차량관성, 저항력, 제동, 배터리 모델로 구성되었다. 또한 현실에서는 운전거동에 따라 동일한 차량 조건에서도 운전자 별로 에너지효율이 다르게 나타난다. 따라서 운전자 특성을 반영할 수 있는 효과적인 운전자 모델이 운전거동의 변화를 반영하기 위해 필요하다. 이를 위해 본 연구에서는 과격성, 인지성, 신경근영향에 대한 인자를 사용하여 운전거동을 모사하는 운전자 모델을 사용하였다. 이러한 운전자 인자들은 확률밀도함수로 표현하여 현실에서 발생하는 효율편차를 가급적 유사하게 반영하고자 하였다. 모터와 변속기의 설계인자는 모터최대토크, 토크분배계수, 변속기어비로 정의하였다. 또한 동적성능과 에너지효율을 정량적으로 표현하기 위해 0-100 km/h 가속시간과 등가연비를 설계 기준으로 사용하였다. 설계인자 값의 변화에 따른 성능과 효율이 크게 변화함을 제시함으로써 우수한 EV 파워트레인 시스템 설계를 위해 이러한 설계인자의 최적화가 필요함을 확인하였다. 일반적으로 성능과 효율개선은 서로 상충되기 때문에 다양한 최적설계안을 제안할 수 있는 다목적 최적화를 수행하는 것이 적합하다. 따라서 본 연구에서는 동적 구속조건을 고려하여 가속시간을 최소화하고 등가연비를 최대화하는 다목적 최적화 문제를 정식화하였다. 확률적 운전자 특성이 반영된 EV 모델을 이용한 다목적 최적화 수행 시 일반적인 최적화 수행 보다 과도한 계산시간이 요구된다. 따라서 인공신경망 알고리즘을 활용하여 가속시간과 등가연비에 대한 대체모델을 구성하였다. 또한 적응적 샘플링 방법을 활용함으로써 최소한의 표본 수로 높은 정확도를 갖는 대체모델을 구성하였다. 대체모델 기반 다목적 최적화를 수행함으로써 성능과 효율이 동시에 고려 된 최적설계안들을 나타내는 파레토(Pareto)해를 제시하고 참고차량 결과와의 비교를 통해 도출된 최적설계안의 우수성을 확인하였다. 또한 결정론적 및 확률론적 운전자 모델 적용 시 각 최적설계안 결과를 서로 비교함으로써 확률론적 운전자 모델의 필요성을 확인하였다. 마지막으로 EV 동적모델과 대체모델 간 계산시간과 해석결과 비교를 통해 대체모델 기반 다목적 최적화의 유효성을 확인하였다.; hence, the specifications of these components should be optimized, to improve both performance and efficiency as much as possible. To analyze such requirements, an EV dynamic model, which includes a two-motor and two-speed powertrain system, was developed using a model-based design methodology. This model consists of driver, powertrain, equivalent vehicle inertia, resistance torque, braking, and battery sub-models. In real-world situations, variations in driver behavior can cause a variation in energy consumption under the same driving conditions. Therefore, an effective driver model, which precisely reflects the driver characteristics, is required to investigate the variation in driver behavior. For realizing this objective, this thesis has employed a driver model that expresses driver behavior using three parameters for the human operator: the aggressivity of driving, the perception of the driver, and the inherent viscosity and inertia of the driver’s muscles. Using a probabilistic approach, these parameters were described by probability density functions. The design parameters for the motors and transmission were defined as the maximum torque of each motor, the torque distribution coefficients between the two motors, and the first and second gear ratios of the transmission. To quantify the performance and efficiency, acceleration time and energy consumption were used as the evaluation criterion, respectively. The results obtained by changing the values of the design parameters show that the specifications of these parameters significantly affect the performance and efficiency of the EV. Therefore, optimizing these parameters is necessary to determine an effective design for the EV powertrain system. Moreover, because of a trade-off between performance and efficiency, a multi-objective optimization method is superior to a single-objective optimization method, for suggesting a variety of design solutions. Accordingly, this thesis formulates a multi-objective optimization problem that minimizes the acceleration time and energy consumption, and that includes dynamic constraints. Because of the large computational effort required to solve the multi-objective optimization problem using the analysis results of the EV model considering the probabilistic driver model, the surrogate models of each objective function were constructed, using an artificial neural network to reduce the computational burden. In addition, by employing an adaptive sampling method, the surrogate models were able to meet the high accuracy requirements of the models, using only a small number of samples to do so. Based on these surrogate models, the multi-objective optimization was performed, and the optimization results provided a Pareto front showing a variety of optimal design solutions that consider both objective functions simultaneously. Through a comparison with the results of a reference design, the superiority of the proposed design was confirmed. Moreover, by comparing the results of the optimal design solutions under both deterministic and probabilistic driver models, the necessity of the probabilistic model was made clear. Finally, comparisons of cost and accuracy between the EV dynamic model and the surrogate model verify the effectiveness of surrogate-based multi-objective optimization.