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An unsupervised machine-learning technique for the definition of a rule-based control strategy in a complex HEV.

ABSTRACT

An unsupervised machine-learning technique, aimed at the identification of the optimal rule-based control strategy, has been developed for parallel hybrid electric vehicles that feature a torque-coupling (TC) device, a speed-coupling (SC) device or a dual-mode system, which is able to realize both actions. The approach is based on the preliminary identification of the optimal control strategy, which is carried out by means of a benchmark optimizer, based on the deterministic dynamic programming technique, for different driving scenarios. The optimization is carried out by selecting the optimal values of the control variables (i.e., transmission gear and power flow) in order to minimize fuel consumption, while taking into account several constraints in terms of N[O.sub.x] emissions, battery state of charge and battery life consumption. The results of the benchmark optimizer are then processed with the aim of extracting a set of optimal rule-based control strategies, which can be implemented onboard in real-time. The input variables of the rule-based strategy are the vehicle power demand, the vehicle speed and the state of charge of the battery. The method for the rule extraction can be summarized as follows. A clustering algorithm discretizes the input domain (in terms of vehicle power demand, vehicle speed and state of charge of the battery) into a mesh of clusters. The generic rule associated to a specific cluster (i.e., the combination of gear and power flow that has to be actuated) is identified by searching for the control strategy most frequently adopted by the benchmark optimizer within the considered cluster. The optimal mesh of clusters is generated using a genetic algorithm technique. Optimal sets of rules are identified for different driving scenarios. These strategies can then be implemented on-board, provided the mission features are known at the beginning of the trip. The main advantage of the proposed technique is that the definition of the rule-based strategy is derived from a machine learning method and is not based on heuristic techniques.

CITATION: Finesso, R., Spessa, E., and Venditti, M., 'An Unsupervised Machine-Learning Technique for the Definition of a Rule-Based Control Strategy in a Complex HEV," SAE Int. J. Alt. Power. 5(2):2016.

INTRODUCTION

Powertrain electrification has increased over the last few years, due to the increasing need to improve the sustainability of the road transport sector, in terms of both energetic and pollutant emission aspects. So far, hybrid electric vehicles (HEV) have been considered as one of the most promising technologies. HEVs are provided with two energy sources, i.e., a battery and a fuel tank, and they are equipped with a conventional thermal engine and one or more electric machines. A significant advantage of HEVs, compared to battery electric vehicles (BEV), is related to their capability of increasing the driving range, as a consequence of the presence of the thermal engine. However, the driving range of HEVs running in pure electric mode is significantly lower than that of BEVs, due to their smaller battery packs. HEVs lead to a reduction in fuel consumption (FC) and C[O.sub.2] emissions, compared to conventional vehicles, mainly due to the reduction in engine size, to the kinetic energy recovery through regenerative braking, to the implementation of the Stop-Start mode and to the possibility of optimizing the power flow from the engine and electric machines [1]. Numerous studies have demonstrated the potential of the hybrid technology to reduce C[O.sub.2] emissions in developing countries [2, 3], which are expected to contribute significantly to greenhouse gas emissions from the transport sector in the near future. A recent study has also shown that the life cycles of C[O.sub.2] emissions of modern HEVs are shorter than those of conventional vehicles [4].

An optimal control strategy to manage the thermal and electric machines is required to fully exploit the potential of hybrid vehicles in order to improve fuel economy and reduce pollutant emissions [5]. The control strategy consists of an algorithm that regulates the operation of the powertrain. It takes input data, such as the vehicle speed, the vehicle acceleration and the road grade, and makes decisions on turning certain components on/off or increasing/decreasing their power output [6]. The control strategy optimization tools that have been developed in recent years can roughly be classified in three categories [7]. The first one includes heuristic control techniques, such as control rules, fuzzy logic and neural networks. These algorithms usually provide an approximate solution to the given optimization problem, but they offer the advantage of requiring a low computational effort. An idea that is commonly employed in heuristic algorithms is the concept of loadleveling, which is based on the shifting of the engine operating conditions to a high efficiency map region and on the utilization of the battery as a load-leveling device, with reference to the model inputs (e.g., the vehicle speed, state of charge of the battery, driver commands). The investigation of fuzzy logic controllers for the design, development and energy management of HEVs has been reported in several studies [8,9,10,11].

The second category of control strategy optimization tools is constituted by static optimization methods. The main concept of these methods involves the identification of the optimal power split between the engine and the electric machine, on the basis of the instantaneous optimization of an equivalent fuel consumption.

The third category of control strategy optimization tools is constituted by dynamic optimization methods, which are based on the modeling of the system dynamics over a defined vehicle mission, and on the minimization of a multi-objective function, which usually includes the cumulated fuel consumption over the entire mission, according to a global optimization approach [12]. The deterministic dynamic programming approach is a well-known dynamic optimization technique that has been widely used in many applications, including those pertaining to the identification of the optimal control strategy in hybrid vehicles. This methodology, which was first presented by Bellman [13, 14], is a multi-stage decision-making process, based on the principle of optimality, which involves a dynamic system, a cost function and control/state grids. Applications based on this technique have been investigated in several papers [14, 15,16, 17, 18, 19],

The main drawback of static optimization methods is that the optimization is performed at each time instant and not globally over a defined vehicle mission. However, the required computational time is limited, and these methods can be suitable for on-board applications. On the other hand, algorithms resulting from dynamic optimization approaches are more accurate under transient conditions, but are also computationally more demanding.

Contribution of the Present Study

The present paper is mainly focused on the development of an unsupervised machine-learning method aimed at the identification of an optimal rule-based control strategy for HEVs. A rule-based control strategy in fact has the advantage of being easily implementable in the vehicle control unit for the real-time optimization of the control strategy; however, traditional rule-based controllers are generally developed and tuned on the basis of engineering experience or heuristic approaches, which might be lacking in performance over a broad range of applications. This study is therefore focused on adopting machine-learning techniques for the extraction of the rules that need to be implemented in the controller.

With reference to the choice of the HEV architecture investigated in this paper, to the best of the authors' knowledge, there is a lack of studies in the literature on dual-mode parallel hybrid electric vehicles, which feature both torque coupling and speed coupling systems, equipped with a compression ignition engine. The hybrid vehicles have been equipped with a diesel engine and an electric machine, which are coupled either via a gearbox (torque coupling) or via a planetary-gear set (speed coupling). The two mechanical connections enable the engine operating point to be shifted either horizontally (speed) or vertically (torque) in the engine map during hybrid operation, and this allows more degrees of freedom to be included for the control strategy optimization. The performance of this vehicle layout has been compared with two parallel configurations that feature either the torque coupling or speed coupling functions separately.

Plug-in HEVs have the potential of further reducing fuel consumption, as well as pollutant and C[O.sub.2] emissions, compared with non-plug-in HEVs [20, 21, 22]. However, the incremental battery cost of plug-in HEVs might not be counterbalanced by the fuel cost savings, as shown in [23], A non-plug-in HEV has therefore been analyzed in this paper. Two different engines have been considered, in order to investigate the impact of the degree of hybridization on such a vehicle architecture.

In general, the identification of an optimal control strategy in hybrid vehicles is of fundamental importance to exploit their potential in order to reduce fuel consumption and pollutant emissions. The control variables that have been selected for this study are the power flow, which is related to the management of the traction power between the thermal and the electric machine, and the gear number of the transmission; the control strategy optimization has the aim of minimizing an objective function, which takes into account the cumulated fuel consumption, the N[O.sub.x] emissions and the battery aging effect. N[O.sub.x] emissions are in fact a major issue in diesel engines, and taking into account battery aging is crucial in order to avoid too aggressive strategies that could lead to an excessive battery depletion, with a consequent increase in the operating costs of the HEV related to the battery replacement. A zero-dimensional model of the vehicle has been developed in the Matlab environment [24] in order to evaluate the evolution of the fuel consumption and of the state of charge (SOC) of the battery, as a function of the vehicle velocity, of the road slope and of the control variables. A global optimizer, which is based on the deterministic dynamic programming theory, has been used to identify the benchmark solution of the optimal control strategy. The outcomes of the proposed rule-based controller, which is based on machine-learning tuning, have been compared with the benchmark optimizer.

This method can be summarized as follows. First, for a given vehicle mission, the optimal control strategy is identified using the benchmark optimizer. A 3D input domain, constituted by the vehicle velocity, vehicle acceleration and state of charge of the battery, is then generated and discretized, so that a grid of input clusters (whose geometrical shape is of parallelepiped type) is obtained. The most frequent action taken by the benchmark optimizer is then selected for each cluster and stored as the rule of the controller for that specific cluster. The optimal discretization grid for the 3D input domain is selected using a genetic algorithm technique. The proposed tool has therefore been referred to as CORE (clustering optimization rule extraction). The resulting rule-based controller can easily be implemented in the vehicle control unit, in order to perform an onboard optimization of the control strategy.

A previously developed mathematical technique has been used in this study in order to decrease the computational time of the benchmark optimizer and of the rule extraction process. In short, the control variables of the problem were discretized, and the values of the main model variables (i.e., instantaneous fuel consumption, battery electric power,...) were evaluated for all of the possible combinations of the control variables and for each time node, and stored in a separate matrix (referred to as 'configuration matrix') for each variable, before the optimization process was started. In this way, the optimizers are able to directly read the actual values of the relevant variables from the preprocessed data, i.e. the configuration matrices, instead of having to calculate them iteratively during the optimization stage. This approach has led to a great computational time saving. The simulations were carried out over a set of driving cycles that includes the New European Driving Cycle (NEDC), three Artemis Driving Cycles and an internally-developed test cycle (TC4).

POWERTRAIN DESIGN

The layout of the hybrid vehicle considered in the present study is reported in Fig. 1: this architecture is here referred to as Dual-Mode Vehicle (DMV). A planetary gear set (PG) and a gearbox (GB) have been installed as speed-coupling and torque-coupling devices, respectively. The engine (E) is connected to the first shaft of the GB and to the PG ring, the electric machine (EM) is connected to the second GB shaft and to the PG sun, the driveline is connected to the PG carrier. Two different clutches have been inserted in order to enable either the speed-coupling mode, if the clutch C1 is engaged and clutch C2 is released, or the torque-coupling mode otherwise. The driveline is depicted in yellow and consists of the transmission (TR) and of the final drive (FD). The battery is connected to the electric machine through the inverter (Inv). This architecture features both torque coupling and speed coupling systems.

In addition to the layout shown in Fig. 1, two additional vehicle architectures have been considered, i.e., the torque-coupling vehicle (TCV) and the speed-coupling vehicle (SCV). They are particular cases of the DMV, in which only the gearbox or the planetary-gear set are present, respectively.

VEHICLE MODEL

Components

Engine

Two different engines have been employed in this study. The first engine, which is here referred to as engine Dl, is a 1.7 L Euro 5 GM prototype diesel engine that is capable of providing a maximum power of 97 kW at 3700 rpm and a maximum torque of 304Nm at 2400 rpm. The second engine, which is here referred to as engine D2, is a 1.3 L Euro 5 GM prototype diesel engine that is capable of providing a maximum power of 70 kW at 4000 rpm and a maximum torque of 206 Nm at 1800 rpm. The adoption of engines that feature different power outputs is of fundamental importance in order to investigate the impact of the degree of hybridization on the performance of the hybrid vehicle.

The performance of the engine was modeled using experimentally-derived look-up tables. The mass flow rate of both fuel and N[O.sub.x] emissions were evaluated by interpolating a 2D map, which is a function of the engine power and speed. The corresponding C[O.sub.2] emissions have instead been linearly determined as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

where [rho] is the fuel density, [[??].sub.fc] is the fuel mass flow rate and 2.65 represents a conversion factor. The latter was obtained considering a combustion reaction of diesel oil with air, such as the one presented in [25], and taking into account an average composition of the fuel from literature data [26],

Electric Machine

The electric machine model simulates the power conversion from the electric to the mechanical form, and vice-versa, taking into account the energy losses by means of efficiency maps, which are functions of the machine power and speed. The electric machines that have been considered in the present study belong to the brushless permanent magnet electric motor/generator family, and all the data were taken from the official website of UQM Technologies [27].

Battery

Lithium-ion batteries have been adopted in this study as the secondary power storage device. The battery model is represented by an equivalent resistance circuit, in which the resistance and the open-circuit voltage of the battery are SOC-dependent. This has allowed a lumped representation of more complex chemical processes to be realized. The battery temperature was assumed to be constant and the temperature effect was therefore disregarded. The SOC represents the electrical status of the battery and depends on the equivalent battery capacity [C.sub.bat] and on the flowing current [I.sub.bat], as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

The battery SOC has been limited within the [0.4-0.8] range, while the maximum current that may be transferred through a cell was established as 120A.

A phenomenological damage accumulation model, based on the concept of "accumulated Ah-throughput" (i.e. the total amount of electrical charge, in both charging and discharging modes, which can flow to or from the battery before it reaches the end of life) has been adopted to estimate the depletion of the battery life. The parameter X, which represents the effective Ah-throughput, can be computed as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

This parameter represents the amount of charge that would have to be exchanged when a nominal cycle is adopted in order to have the same aging effect as the actual cycle the battery has undergone. The severity factor a represents the relative aging effect, with respect to the nominal cycle, and it is higher than 1 for severe aging conditions (i.e. which would lead to a shorter life). The severity factor is estimated as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

The residual battery life [[lambda].sub.r] which represents the fraction of charge that could still flow through the battery before the end of its life, is determined as follows:

[[lambda].sub.r] = 1-[[lambda]/[LAMBDA]] (5)

where [LAMBDA] is the battery life, which has here been set to 20000 Ah. The end of life condition is defined as the instant at which [[lambda].sub.r] = 0.

Torque-Coupling and Speed-Coupling Devices

A mechanical torque-coupling device has been employed to couple the torque that is obtained from two different power sources (i.e., the engine and the electric machine) and to provide the resulting torque to the output shaft. A two-shaft type gearbox has been used in this study, as shown in Fig. 2 (top). The speed ratio is defined as [[tau].sub.tc] = [[z.sub.1]/[z.sub.2]] = [[R.sub.1]/[R.sub.2]], where [z.sub.1] and [z.sub.2] are the number of teeth of the corresponding gear, while [R.sub.1] and [R.sub.2] are the radii of the corresponding gear. The speed correlation is written as follows:

[[omega].sub.out] = [[omega].sub.in,1] = [[omega].sub.in,2]/[[tau].sub.tc](6)

With reference to the free body diagram, the torque correlation between the shafts is obtained as follows (if losses are ignored):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)

A mechanical speed-coupling device has instead been employed to couple the speeds of two different power sources that enter the device separately (through two distinct shafts) and to provide the resulting torque to the output shaft. A planetary gear unit, which mechanically connects the power derived from all the power sources, has been used in this study. This device consists of three rotating nodes, namely a sun gear, a ring gear, and a carrier gear, as shown in Fig. 2 (bottom). These nodes are linked by a few small pinion gears. The speed ratio is defined as [[tau].sub.sc] = [[R.sub.r]/[R.sub.s]], where [R.sub.s] and [R.sub.r] are the radii of the sun gear and the ring gear, respectively. With reference to the Willis method, the speed correlation between the ring gear [[omega].sub.r], the sun gear [[omega].sub.s] the carrier gear [[omega].sub.c] is obtained as follows:

[[omega].sub.s] + [[tau].sub.r] * [[omega].sub.r] = (1 + [[tou].sub.sc]) * [[omega].sub.c] (8)

With reference to the free body diagram, the torque correlations are then determined taking into account the geometry of the device:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)

where [T.sub.s], [T.sub.c] , [T.sub.r], are the torque values of the sun gear shaft, the carrier shaft and the ring gear shaft, respectively.

Transmission

The driveline consists of a 6-speed gearbox (which will be referred to as "transmission" in this study) and of the front final drive. The power losses of the transmission have been estimated by means of an efficiency map, which is a function of the output shaft speed and torque and of the selected gear number. The transmission inertia has been also taken into account. The final drive has instead been modeled as a torque multiplier, while power losses and inertia contributions have been neglected. The transmission speed ratio values are reported in Table 1 for each gear.

Determination of the Power and Speed of the Engine and Electric Machine

The total vehicle power demand [P.sub.v] at the wheel level is the sum of several contributions: the rolling resistance, the grade resistance, the drag resistance and the inertia. The total power demand of the vehicle can be expressed as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (10)

where [m.sub.v] is the vehicle mass, g is the gravitational acceleration, [r.sub.v] is the rolling resistance coefficient of the vehicle, [[alpha].sub.r] is the slope of the road, [V.sub.v] is the vehicle velocity, [A.sub.v] is the front area of the vehicle, [[rho].sub.air] is the air density, [c.sub.x], is the aerodynamic drag coefficient, [R.sub.wh] is the dynamic wheel radius and [I.sub.wh] is the wheel inertia.

The vehicle working condition may be either of a traction type, if the power is positive, or of a braking type, if the power is negative. The power at the final drive level is then determined as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (11)

where the factor [[gamma].sub.fr] represents the power split between the front and the rear wheels of the vehicle during the braking phase, while [[gamma].sub.br] represents the power share that has to be managed by the mechanical frictional brakes during braking. The [[gamma].sub.fr] value has been kept constant and equal to 0.75 for all of the simulations, while the value of [[gamma].sub.br] has been set equal to 0.1.

The power required at the front powertrain level is obtained as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (12)

where [P.sub.tr,in'], [P.sub.e,in] and [P.sub.em,in] are the inertial power of the transmission, of the engine and of the electric machine, respectively, [[eta].sub.tr] is the transmission efficiency, and exponent k is equal to 1, if the vehicle is braking, or equal to -1 otherwise.

The angular velocity [[omega].sub.f] at the front powertrain level is a function of the control variable [tau] as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (13)

where [[tau].sub.fd] is the speed ratio of the final drive.

The formulation used to determine the power of the engine [P.sub.e] and of the electric machine [P.sub.em] is obtained considering the value of the sub-control variable a:

[P.sub.e] = (1 - [alpha]) * [P.sub.f] (14)

[P.sub.em] = [alpha] * [P.sub.f] (15)

As far as the formulation of the speed of the engine and of the electric machine is concerned, two different modes have to be considered.

Mode 1 - Torque Coupling

With reference to Eq. (8), the engine speed is obtained if the sun shaft is blocked:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (16)

where [[omega].sub.e,t] and [[omega].sub.f] are the speed of the engine and of the front powertrain, while [[tau].sub.sc] is the PG speed ratio. The electric machine is now connected to the second GB shaft, and its speed can be defined as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (17)

where [[omega].sub.em,t] is the electric machine speed and [[tau].sub.tc] is the GB speed ratio.

Mode 2 - Speed Coupling

With reference to Eq. (9). the engine power can be expressed as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (18)

where [T.sub.e] and [T.sub.f] are the torque at the engine and at the front powertrain level, respectively, while [[omega].sub.e] and [[omega].sub.f] are the speed of the engine and of the front powertrain and [[tau].sub.sc] is the PG speed ratio. The engine speed is therefore obtained as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (19)

In a similar way, the power of the electric machine can be written as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (20)

where [T.sub.em], [[omega].sub.em] are the torque and the speed of the electric machine, whose speed is calculated as follows:

[[omega].sub.em,s] = a-(l+[[tau].sub.sc]) * [[omega].sub.f] (21)

Determination of the Maximum Power Curve of the DMV

The maximum power curve of the DMV, as a function of the vehicle speed, can be derived as follows. First, it should be noted that the maximum power can be obtained either in torque-coupling mode or in speed-coupling mode. The maximum power that can be delivered in torque-coupling mode is evaluated as follows:

[P.sub.pt,tc] = [P.sub.em,max] ([[omega].sub.em]) + [P.sub.e,max] ([[omega].sub.e]) (22)

where the values of the speed of the electric machine and of the engine are obtained from Eq. (17) and Eq. (16). respectively. The maximum power which can be delivered in speed-coupling mode is obtained by selecting the engine speed [[omega].sub.e] that leads to the maximum power value of [P.sub.pt,sc,] for a specific combination of vehicle velocity [V.sub.v] and of gear number GN, as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (23)

where the electric machine speed stems from Eq. (8). Finally, the GN which maximizes the power at a given vehicle velocity is selected, so that:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (24)

The TC and SC Vehicles

The model equations of the TCV can be obtained from the DMV model if the speed ratio [[tau].sub.sc] [right arrow] [infinity]. The model equations of the SCV can instead be found from those of the DMV, if the speed ratio [[tau].sub.tc] is set to 1.

Control/State Variables and their Discretization

The gear number GN and the power flow PF have been chosen as the control variables in this study. The GN variable determines the speed ratio of the transmission, [tau] (see Table 1). The GN domain is defined by the [S.sub.gn] = {1,2,...,6} set, since a 6-speed transmission has been adopted on the front axle. The PF variable is related to the management of the power of the engine and the electric machine. In particular, it controls the sub-control variable [alpha], which quantifies the power contribution provided by the battery through the front axle, with respect to the front vehicle power demand (see Eqs. (14-15)). The PF domain is defined by the [S.sub.pf] = {1,2,... ,[N.sub.pf]} set, where [N.sub.pf] stands for the number of different power flow types. The default size of [S.sub.pf] has been set equal to 7 for the dual-mode vehicle.

All the different values of the PF control variable are listed in Table 2, where pe stands for pure electric mode, pt for pure thermal mode, ps for power split mode and be for battery charge mode, while tc stands for torque-coupling and sc for speed-coupling.

Two different pure-electric modes are possible for the dual-mode vehicle: the electric machine can in fact drive the vehicle either in torque-coupling mode (pe.tc) or in speed-coupling mode (pe.se). Only one pure-thermal mode is possible for this vehicle layout, where both the electric machine clutches are disengaged and the engine is connected to the driveline in the torque-coupling mode.

Finally, the electric machine can work either to assist the engine or to charge the battery, and it can be connected either in speed-coupling mode or in torque-coupling mode. The power of each component is identified according to the value of the sub-control variable [alpha] (see Eqs. (14-15)). The speeds of the engine and of the electric machine are obtained by means of Eq. (19) and Eq. (21). respectively, if the speed-coupling mode is enabled, otherwise by means of Eq. (16) and Eq. (17). respectively, if the torque-coupling mode is selected.

With reference to the state variables, the state of the engine, which can be equal to 0 if the engine is off, or equal to 1 otherwise (the related discrete set is therefore [S.sub.es] = {0, 1}), was chosen as the first variable. The battery SOC was chosen as the second state variable. It can vary in the [S.sub.soc] = {0.4, 0.4001,...,0.8} discrete set, since 4000 discretization steps have been considered. While the evolution of the battery SOC depends on the time-history of the two control variables, the engine state is obtained directly as a function of the instantaneous value of the power flow.

Time Grid Discretization

The time domain has been discretized uniformly with a time step of 3 s in order to create the corresponding time grid. To this end, the vehicle model equations were written considering separate formulations for the left and right sides of each time node, in order to reduce the errors in the evaluation of the cumulated quantities (such as FC and SOC). The introduced procedure leads to an interval-grid domain, which replaces a node-grid approach. This approach was introduced in [28] and has resulted in a significant reduction in the simulation time and memory requirement, as a refined time domain discretization is not required.

Configuration Matrix Approach

Two different definitions for the powertrain configuration have here been introduced. The first configuration, [C.sub.pt], is defined as a combination of the sets of actions, namely [S.sub.gn] and [S.sub.pt'] and the two sets of the states, namely [S.sub.es] and [S.sub.soc], and is expressed as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (25)

This definition is used to uniquely define the powertrain configuration at each time instant t; however, it should be noted that the variable [v.sub.2] (i.e., the state of charge of the battery) is a function of the specific control strategy adopted in the time interval (0, t). A second definition of the powertrain configuration (i.e., [C.sub.pt\bat]), which does not take into account the battery state, is provided as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (26)

This definition is also referred to as [C.sub.pt]'. Its advantage is that it is independent of the time history of the control variables in the time interval (0, t). This definition has suggested the development of a mathematical technique (defined as "Configuration matrix approach", see [28]), that has allowed the computational time required by the optimizers to be reduced to a great extent. In short, the values of the main model variables (i.e., speed and input/output power of each component of the powertrain, fuel consumption and N[O.sub.x] emissions), except for the battery SOC (i.e., the variable [v.sub.2]) were evaluated for all of the possible combinations of the discrete values of [u.sub.1] [u.sub.2] and [V.sub.1] in Eq. (26), and stored in a separate matrix (referred to as 'configuration matrix'), before the optimization process was started. In this way, the optimizers were able to directly read the actual values of the relevant variables from the preprocessed data, instead of having to calculate them iteratively during the optimization stage. The battery SOC is instead estimated from the battery model equation during the optimization process, as it depends on the control strategy.

The configuration matrix approach allows the number of model evaluations to be reduced by a factor that ranges from [10.sup.2] to [10.sup.3], depending on the specific optimizer. It was verified that the elaboration of all the configuration matrices during the preprocessing stage only requires a few seconds in the Matlab environment, when a computer that features an Intel i7 processor (8 CPUs at 2.8 GHz) and 16 GB of RAM is used.

Feasible Set of Control Variables

Not all the powertrain configuration combinations lead to feasible results. A set of constraints has therefore been introduced, in order to identify the feasible combinations of the GN and PF control variables that have to be considered in the configuration matrix approach, as follows:

1. During the braking stages, the power share that the engine should manage has to be zero.

2. The angular velocity of the electric machine and the engine has to be within the feasible working range. In addition, if the engine is running and the associated speed is less than the idle speed, the GN has to be equal to 1.

3. The power that has to be provided by each component has to be within the feasible working range.

4. The engine can be launched if and only if the electric machine and the battery working as the power source are able to accelerate the engine up to the coupling speed.

5. In the optimization stage, the battery power has to be within the feasible working range, which is a function of the current value of the battery SOC.

IDENTIFICATION OF THE OPTIMAL CONTROL STRATEGY

Objective Function

The optimal policy or control strategy u*(t) is determined by minimizing an objective function, J, while the constraint on the final SOC has to be guaranteed (i.e., the SOC at the end of the mission has to be higher or equal to that at the beginning, as the architecture is of the non-plug-in type). The mathematical formulation of the problem is:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (27)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (28)

where u(t) is the generic policy or control strategy and S*(t) is the set of feasible combinations of control variables for each time interval t; [SOC.sub.end] is the battery SOC at the end of the mission and [SOC.sub.0] is its initial value. S*(t) is a subset of the set of all the combinations of the control variables.

If the after-treatment devices are not sufficient to meet the emission limits, the engine-out N[O.sub.x] levels should be controlled directly by means of the control strategy. Similarly, the cost of battery life depletion might become extremely significant if a control strategy optimization is completely oriented towards a reduction in fuel consumption. A term has therefore been inserted into the J definition in order to take into account the effects of aggressive power management strategies on battery aging. The objective function has been defined as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (29)

where FC is the cumulated mass of fuel consumed over the mission (kg), [FC.sub.rv] is the cumulated mass of fuel consumed by the reference vehicle (kg), N[O.sub.x] and N[O.sub.x,ds] are the cumulated nitrogen oxide mass emissions of the hybrid vehicle and of the reference vehicle equipped with the same downsized engine, respectively (kg), BP is the cost related to battery replacement ($), FP is the fuel price ($/kg), [lambda] is the effective battery life consumption (Ah) and A is the battery life (Ah).

Three weighting factors have been introduced, namely [[alpha].sub.1] [[alpha].sub.2] and [[alpha].sub.3], in order to adjust the relative importance of the related terms. This formulation allows the fuel consumption, the N[O.sub.x] emissions and the battery life depletion effects to be taken into account at the same time.

Dynamic Programming

Dynamic programming (DP) has been adopted as the benchmark method to optimize the control strategy. DP is a well-known optimization technique that has been used extensively in many applications, including those adopted for the identification of the optimal control strategy in hybrid vehicles. Details on this technique and its applications can be found in [13, 14, 11, 16, 12, 18, 12, 28].

Clustering Optimization Rule Extraction (CORE) Tool

The machine-learning-based optimizer that has been developed in the present study has the aim of extracting an optimal set of rules, for a given vehicle mission, on the basis of the optimal control strategy that was first identified by means of the benchmark optimizer.

A 3D input domain, constituted by the vehicle velocity, vehicle acceleration (which is related to the vehicle power demand) and the battery SOC, is generated and discretized, so that a mesh of input clusters is obtained. The most frequent action taken by the benchmark optimizer is then selected for each cluster and stored as the rule of the controller for that specific cluster. The optimal discretization of the 3D input domain is obtained using a genetic algorithm (GA) technique. The proposed tool has therefore been referred to as CORE (clustering optimization rule extraction).

From a mathematical point of view, this tool defines an optimal deterministic finite automaton that is suitable for implementation in a rule-based controller for onboard control strategy optimization. The finite automaton consists of a finite set of input states, a finite set of output states and a rule. The latter has to connect the input states to the output states. The vehicle velocity, the vehicle acceleration and the battery SOC have been selected as the input variables, and their discretization represents the input states, while the discretization of the two control variables, GN and PF, generates the output states.

The logical steps of the CORE tool are described hereafter.

Rule Identification

First, the benchmark optimizer is applied to a vehicle mission to identify the optimal control strategy, in terms of GN and PF, which minimizes the objective function defined by Eq. (29). The time histories of the vehicle velocity, vehicle velocity variation and SOC of the battery are thus identified and can be used as input variables of the CORE tool.

The 3D domain of the three input variables is then discretized into clusters. Figure 3 reports an example in which the vehicle velocity, the velocity variation and the state of charge of the battery have been discretized into 5, 4 and 3 non-equispaced levels, respectively, so that a total number of 60 clusters are generated. The identification of the mesh, in terms of number of clusters and discretization length, will be discussed in the "Optimal discretization of input variable domain by means of GA solver" and "Results and discussion" sections (see Fig. 20).

Each point of the vehicle mission is then represented in the 3D domain and associated to a specific cluster, as shown in Fig. 3. It should be noted that, in general, not all the clusters will include vehicle mission points.

Once the points of the vehicle missions have been associated to the clusters, the control strategy obtained with DP is analyzed by the CORE tool, and the most frequent action is extracted from that control strategy for each cluster and is stored as the rule of the controller for that specific cluster. For example, let us consider the points belonging to a generic cluster C (colored points in the left parallelepiped in Fig. 4). Each color identifies a specific action (e,g., green for pure electric mode, blue for power split mode, red for pure thermal mode and yellow for battery charge mode) that has been taken by DP for that specific point. The most frequent action that has been taken by the benchmark optimizer for the points belonging to the considered cluster C is then selected as the rule for that cluster (e.g., power split mode for the C cluster represented in the parallelepiped on the right in Fig. 4) It should be noted that only four generic actions (i.e., pure electric, power split, pure thermal, battery charge) have been reported in Fig. 4 for the sake of simplicity. However, the rule associated to the generic cluster C contains specific information pertaining to the gear number and power flow, which corresponds to the most frequent combination adopted by the benchmark optimizer for that cluster.

If no combination of the three input variables (i.e., vehicle velocity, velocity variation and battery SOC) appears over the mission in a specific cluster, the system introduces a callback for simple backup rules (e.g., battery charging at low SOC, battery discharging at high SOC, or pure thermal mode). This is represented by the grey cluster in the right parallelepiped in Fig. 4.

Optimal Discretization of the Input Variable Domain by means of the GA Solver

The performance of the rule-based method is expected to be correlated to a great extent to the discretization of the 3D input variable domain. For example, if a different discretization is introduced, some points of the vehicle missions might no longer belong to the same cluster as that of the original discretization. Moreover, it should also be noted that if a too refined discretization is introduced, a high number of empty clusters (i.e., clusters that do not include vehicle mission points) would be generated, and this would result in the need for a high number of backup rules.

For this reason, a stochastic solver, which is based on the genetic algorithm (GA) theory [29, 30, 31], has been used to define the best size of the grid for each input variable (i.e., the optimal mesh size of the parallelepiped at the bottom of Fig. 3).

In general, the selected GA solver identifies an initial population of random individuals. The genome of the generic individual of the GA solver defines the [N.sub.k] grid lengths of the three input variables. The population evolves generation by generation, according to mutation and crossover mechanisms [29, 30, 31], and in the end the best individual is selected. The GA structure of this specific application is illustrated in Fig. 5, where an example of a generic individual is proposed. The individual, K, consists of three sections, namely [K.sub.1] [K.sub.2] and [K.sub.3], one per each input variable (colored in blue, yellow and green for vehicle velocity, velocity variation and battery SOC, respectively, as shown in Fig. 5a). The individual dimension [N.sub.k] (9 in this example) is fixed during the GA optimization. The vehicle velocity grid, [G.sub.1] is discretized into [N.sub.k,1] + 1 segments, according to the blue [N.sub.k,1] elements of [K.sub.1] Similarly, the velocity variation and the battery SOC are discretized into [N.sub.k,2] + 1 and [N.sub.k,3] + 1 segments, respectively, hence the yellow [N.sub.k,2] elements of [K.sub.2] are selected for the second grid, while the green [N.sub.k,3] elements of [K.sub.3] are chosen for the last grid. The numbers in each element of the individual in Fig. 5a represent the length of the discretizated grid intervals. The extreme values of the grid are selected for each input variable according to the specific application. For instance, the vehicle velocity ranges for [R.sub.1] = [0,100] km/h, the velocity variation for [R.sub.2] = [-20,20] km/h/s, while the battery SOC for [R.sub.3] = [0.4,0.8] (see Fig. 5b). As an example, let us focus on the grid definition for the first input variable (i.e., the blue elements of the individual in Fig. 5b). Given [K.sub.1] = [20,5,20,25], the grid [G.sub.1] is an array of [N.sub.k,1] + 2 elements, where the first [N.sub.k,1] + 1 elements are determined as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (30)

while the last element [G.sub.1]([N.sub.k,1] + 2) is the rightmost value in the [R.sub.1] range, i.e. [R.sub.1](2). In this example, the grid is obtained as [G.sub.1] = [0,20,25,45,70,100]. Since the [G.sub.1] grid is now known, it is possible to discretize any value of this input variable. For example, a velocity of 53 km/h belongs to the fourth grid level. This procedure has to be applied in a similar way to the second and third input variables in order to obtain the [G.sub.2] and [G.sub.3] grids.

The procedure is carried out for each individual of the population.

The performance of the rule-based optimizer, which is obtained using the specific individual generated by the GA solver (i.e., a specific grid size configuration), and the associated set of rules (using the procedure explained in Figs. 3-4), is then evaluated. To do this, each individual is assigned a score, according to the objective function defined in Eq. (29) (see Fig. 5c), which receives the cumulated FC and N[O.sub.x] emissions and the battery life consumption [lambda] as input. At the end, the GA selects the individual (i.e., the optimal grid size) that provides the best score.

Further Considerations on CORE Tool Implementation

In this study, the default discrete non-equispaced intervals of the grids for the three variables were set to 9, 9 and 3 for the vehicle velocity, vehicle velocity variation and battery SOC, respectively (hence [N.sub.k,1] = [N.sub.k,2] = 8, [N.sub.k,3] = 2). This choice is the result of a sensitivity analysis of the mesh dimension, whose results are shown in the "Results and discussion" section (see Fig. 20). The resulting 3D input domain is a mesh of [N.sub.r] clusters ([N.sub.r] = 9 * 9 * 3 = 243). However, the number of [N.sub.r] clusters is equal to 60 in the simplified 3D input domain represented in Fig. 5.

The genome of a generic individual of the GA solver is an [R.sup.1xNk] array (as already shown in the simplified example in Fig. 5a). In this investigation, the default number of terms is [N.sub.k] = (9 - 1) + (9 -1) + (3 -1) = 18. For the simplified 3D input domain represented in Fig. 5. the individual size [N.sub.k] is (5 - 1) + (4 - 1) + (3 -1) = 9. Therefore, the tool initially has to generate a population, [pi], that is, an [R.sup.NmdxNk] matrix, where [N.sub.ind] is the number of individuals that will evolve for [N.sub.g] generations on the basis of mutation ([[micro].sub.0], [[micro].sub.1]) and crossover ([chi]) mechanisms. The values that have been assigned to the main parameters of the GA are listed in Table 3. The population dimension has been chosen to be two orders of magnitude greater than the length of the individual, and the generation number has been tested in terms of solution convergence, while the other parameters have been maintained constant.

An example of score evolution during the training of the CORE tool over the AUDC mission is instead reported in Fig. 6. It can be seen from the chart how the score stabilizes after about 30 generations.

Onboard Application of the Rule-Based Method

The identified set of rules can easily be implemented in a real engine control unit for onboard applications. In fact, the cluster that includes the generic point of the vehicle mission (in terms of vehicle velocity, velocity variation and battery SOC) is identified at each time instant, and the associated rule is then applied.

The required computational time is very low, as it is basically constituted by the time required by the ECU to read the rule from the matrix that has been stored in the ECU itself.

RESULTS AND DISCUSSION

Model Assessment

The models of the different components, i.e., the engine, the electric machine and the battery, have been assessed by means of experimental tests carried out on a diesel mild hybrid powertrain equipped with a belt-alternator starter installed at the dynamic test bed of the ICEAL-PT (Internal Combustion Engine Advanced Laboratory, Dipartimento Energia, Politecnico di Torino). For further details on the test rig specifications, the reader can refer to [32], and for further details on the assessment of the model, the reader can refer to [33, 34, 35]. All the data concerning the efficiency of the components have been normalized, for intellectual property reasons.

Driving Mission

The performance of the hybrid vehicles analyzed in this study has been evaluated over a set of five driving missions. The main specifications of the driving cycles are shown in Table 4, which reports the duration T, the covered distance D, the global average velocity [bar.V.sub.V], the effective average velocity [bar.V.sub.V]', the maximum velocity [V.sub.v,max] the maximum vehicle powers [P.sub.tr,max] and [P.sub.br,max] for the traction and braking stages, respectively, the average vehicle powers [bar.P.sub.tr] and [bar.P.sub.br], as well as the total energy demands [E.sub.tr] and [E.sub.br] for the traction and braking stages. Figure 7 reports the coordinates of each driving mission, where the x-axis indicates the average speed, while the y-axis represents the ratio of the traction energy demand and the covered distance. This picture provides useful information to help understand which driving missions are more demanding in terms of energy and velocity.

Vehicle Analysis

The vehicle is characterized by a drag coefficient [c.sub.x] of 0.3, front area [A.sub.v] of 2 [m.sup.2], a tire radius of 0.327 m and a chassis mass of 1250 kg. The size of the components of each vehicle are reported in Table 5 for both the D1 and D2 engines, while the main specifications of each vehicle, in terms of total mass, performance index (PI), cost and payback distance, are reported in Fig. 8. The layout of each vehicle has been optimized using the tool developed in [28].

The total mass of the hybrid vehicles resulted to be of the same order as that of the conventional vehicle. It in fact ranges from 1523 kg to 15 30 kg for the vehicles equipped with the D1 engine, and from 1510 kg to 1523 kg for the vehicles equipped with the D2 engine, while the total mass of the reference vehicle is 1536 kg. This is due to the power density of the battery, which is significantly high for non plug-in hybrid vehicles (i.e., twice the specific power of a conventional vehicle engine). The SCV, equipped with the Dl engine, resulted to have the highest weight, while DMV-D2 had the lightest. The vehicle performance capability has been measured as a combination of the acceleration time, elasticity time and time necessary to travel 1km over different uphill roads at the maximum velocity. The sum of these time intervals is defined as the performance index (PI). The total costs have been estimated taking into account both the production and operating contributions. The production costs include the cost of the engine, of the electric machines and of the battery pack. The operating costs are the sum of the costs related to the battery depletion and the costs of the required fuel, over the TC4 mission, for ten years in which a total distance of 250000 km is covered. In general, vehicles equipped with the D2 engine are capable of reducing the total costs by 2.5%, with respect to the corresponding vehicles equipped with the D1 one, except for SCVD2 (5%). The maximum cost reduction, with respect to the reference vehicle, is obtained for DMV-D2 (17.7%). A low payback distance can therefore be expected for this type of architecture. In general, the cost saving also depends on the distance covered by the vehicle: the longer the distance, the greater the operating cost reduction with respect to a conventional vehicle. The payback distance represents the distance that each vehicle has to cover to counterbalance the initial investment due to the operating cost saving. The average payback distance over TC4 is 102000 km, 134000 km and 94000 km for the TCV, SCV and DMV equipped with the Dl engine, respectively, while it is 99000 km, 118000 km and 91000 km for the same vehicles equipped with the D2 engine. The hybrid architecture is convenient if the operating cost saving over the vehicle life, with respect to the conventional vehicle, is able to balance or overcome the production cost increase, i.e., the cost of the initial investment.

Figure 9 reports, for the three hybrid vehicles equipped with both the D1 and D2 engines, the FC reduction with respect to the reference vehicle (top left), the N[O.sub.x] emission reduction with respect to the pure-thermal strategy (top right), the number of batteries employed (bottom left) and the total cost (bottom right), over the set of driving cycles. Each single driving mission has been repeated in order to cover a total distance of 250000 km. The average cumulated C[O.sub.2] emissions over the different missions are also reported in the top-left section. It is worth highlighting that, for each hybrid vehicle and mission, the N[O.sub.x] emission reduction refers to the case in which the same mission is run by the hybrid vehicle using a pure-thermal strategy. This allows the impact of the hybrid operating strategy on the N[O.sub.x] emissions to be verified directly on a given hybrid vehicle. The results shown in Fig. 9 were obtained using the benchmark optimizer (i.e., DP) and an FC-N[O.sub.x]-BLC-oriented optimization. In short, the three factors in Eq. (29) have been set as follows: [[alpha].sub.x] = 0.45, [[alpha].sub.2] = 0.1, [[alpha].sub.3] = 0.45. It can be seen, in the figure, that DMVD2 is the best choice of vehicle to reduce the total costs (15.7 k$); the average FC improvement for the same vehicle is 34.9%, while the average C[O.sub.2] emissions are 109 g/km. If C[O.sub.2] emissions are a major concern, SCV-D2 should be taken into account (101 g/km). However, the use of this vehicle leads to a greater battery life depletion than DMV-D2 (1.4 batteries employed vs 0.8), which in turn leads to an increase in the total costs. SCV-D2 is also able to reduce the N[O.sub.x] emissions to a great extent (43.7%). In general, SCVs lead to a more pronounced battery life depletion, while DMVs lead to the less depletion. Since the battery costs are still a major concern in HEVs, the hybrid architectures that lead to a moderate battery aging depletion show the greatest potential to reduce the overall costs. It should be noted that if lithium-ion technology is improved in terms of life duration and/or cost per energy content, more aggressive battery usage strategies could be adopted to further decrease C[O.sub.2] and N[O.sub.x] emissions.

It is worth recalling that the N[O.sub.x] emission levels have been inserted into the optimization process, in order to avoid an excessive deterioration with respect to the case in which the vehicle is only driven by the engine. If the control strategy were optimized without taking into account the cumulated N[O.sub.x] emissions, extremely high emission values would likely be reached, especially for the vehicles equipped with the D2 engine. This disappointing result is due to the fact that the standard calibration maps of the engines considered in the present study have not been optimized for a hybrid application. To avoid this issue, a comprehensive optimization tool, which is capable of identifying not only the optimal control strategy of the hybrid powertrains over the mission, but also the optimal values of the main engine parameters (i.e., EGR rate, start of injection), is currently being developed. This tool will incorporate specifically developed low-throughput models that simulate the combustion and emission formation processes in the engine (see [32, 36, 37, 38, 39]). The results of this research will be presented in the near future.

Finally, it is interesting to investigate how the residual battery life is affected by the control strategy. For example, the most demanding case, in terms of battery life consumption, is given by the use of SCV-D1 over the AUDC (4 batteries are required during the vehicle's life, see Fig. 9). while the least demanding one is that pertaining to the use of DMV-D2 over the AMDC. Since the key-strategy typically used for hybrid vehicles over urban-like driving scenarios is to shift the engine operating point to either the fuel-optimal operating region or the N[O.sub.x]-optimal operating area, and since it has been verified that the two regions are closer in the engine map of the D2 engine than in that of the D1 one, it is not surprising that a significant battery usage can be observed when the D1 engine is employed in urban missions. On the other hand, it has been verified that the D2 engine (which is smaller than the Dl one) features an overall good efficiency map that leads to a more moderate battery usage, especially over a highway driving mission such as AMDC.

Figure 10 reports the time history of the battery SOC for TCV (solid blue line), SCV (dashed red line) and DMV (dashed green line), equipped with the D1 (left) and D2 (right) engines, using the FCBLC-oriented optimization. The simulations results over NEDC (top), AUDC (middle) and AMDC (bottom), obtained using the benchmark optimizer, are shown in the figure. Two key-parameters that are related to battery usage are the overall battery life residual [[lambda].sub.r] (which is reported in Fig. 9) and the maximum variation of the state of charge over the mission, i.e., [DELTA]SO[C.sub.max]. As far as the results over AMDC are concerned, the minimum cost is achieved by TCV-D2 (17.4 k$, see Fig. 9). In this case, the battery has been employed so that [[lambda].sub.r] and [DELTA]SO[C.sub.max] are equal to 44% (i.e., it is not necessary to replace the battery over this mission) and 5%, respectively, and the vehicle is able to achieve 126 g/km of C[O.sub.2] emissions. As far as AUDC is concerned, the minimum cost is achieved by DMV-D2 (i.e., 18.3 k$). In this case, the battery has been employed so that [[lambda].sub.r] and [DELTA]SO[C.sub.max] are equal to -55% (i.e., one battery replacement is needed over the mission) and 1%, respectively, and the vehicle is able to achieve 123 g/km of C[O.sub.2] emissions. Finally, as far as NEDC is concerned, the minimum cost is achieved by DMV-D2 (i.e., 13.6 k$); in this case the battery has been employed so that [[lambda].sub.r] and [DELTA]SO[C.sub.max] equal to 24% and 3%, respectively, and the vehicle is able to achieve 91.5 g/km of C[O.sub.2] emissions. The most interesting case regards DMV-D2 over AUDC, where the battery is adopted intensively to drastically reduce fuel consumption (this reduction is of 50.9% with respect to the reference vehicle, and the battery life residual is -55%), even though the battery SOC is maintained around the initial state of 0.7 (see Fig. 10, middle-right chart, green dashed line curve).

Analysis of the Effects of Different Oriented Optimizations

Eight cases have been selected in order to investigate the impact of different oriented optimizations on the performance of the hybrid vehicle. The results over the NEDC and AUDC missions obtained using DMV, equipped with both Dl and D2 engines, were selected for this analysis. Three oriented optimizations have been investigated, i.e.: FC-N[O.sub.x]-BLC-oriented, where [[alpha].sub.1] = 0.45, [[alpha].sub.2] = 0.1, [[alpha].sub.3] = 0.45 FC-BLC-oriented, where [[alpha].sub.1] = 0.5 [[alpha].sub.2] = 0, [[alpha].sub.3] = 0.5, and N[O.sub.x]-oriented, where [[alpha].sub.1] = 0,[[alpha].sub.2] = 1, [[alpha].sub.3] = 0. Table 6 reports the details of the different investigated cases.

Figure 11 reports the overall C[O.sub.2] emissions (top left), the N[O.sub.x] emission reduction with respect to the pure-thermal strategy (top right), the number of batteries employed (bottom left) and the total costs (bottom right). The results obtained with DP (blue bars) and CORE (red bars) tools have been reported for this analysis, in order to make a preliminary evaluation of the performance of the rulebased optimizer proposed in the present study. The impact of the different oriented optimizations on the DMV-D2 performance over NEDC can be investigated by comparing cases 2, 5 and 7 (see Table 6). If the N[O.sub.x] emissions are not taken into account (i.e., the FC-BLC-oriented-optimization, case 5), the C[O.sub.2] emissions are only improved by 1 g/km with respect to the FC-N[O.sub.x]-BLC one, and the costs remain unchanged. However, the N[O.sub.x] emission reduction decreases from 63% to 11%. If the N[O.sub.x]-oriented optimization (i.e., case 7) is compared with the FC-N[O.sub.x]-BLC-oriented one (i.e., case 2), it can be noted that an additional 11% of N[O.sub.x] emission reduction can be achieved, but at the expense of an increase in C[O.sub.2] emissions of the order of 6 g/km. This also leads to an increase in the overall costs of the order of 3.5 k$. As far as AUDC is concerned, the same trend is observed from a comparison of the FC-N[O.sub.x]-BLC-oriented optimization (i.e., case 4) and the FC-BLC-oriented one (i.e., case 6). However, if the N[O.sub.x]-oriented optimization (i.e., case 8) is compared with the FC-N[O.sub.x]-BLC-oriented one, it is can be seen that the N[O.sub.x] emission reduction increases by 38 percentage points, but the C[O.sub.2] emissions also decrease by 17 g/km. This means that, in the FC-N[O.sub.x]-BLC-oriented optimization, the selected operating strategy tends to avoid excessive battery usage, at the expense of a less effective C[O.sub.2] emission reduction. The dual positive effect obtained using the N[O.sub.x] oriented optimization is counterbalanced by an extremely high consumption of battery life, thus the costs increase by 5.4 k$.

A very important result that is shown in Fig. 11 is that the results of the proposed rule-based optimizer are very close to those of the benchmark one.

Figure 12 reports the distribution of the working modes of the hybrid vehicle (i.e., power split, pure thermal and battery charge) on the engine map, for the first four cases mentioned in Table 6. The results obtained with DP are shown in the left column, while those obtained with CORE are reported in the right column. The optimal operating line, in terms of fuel economy, has also been reported as a dashed green line in each plot, while the optimal operating line, in terms of N[O.sub.x] emissions, is reported with a dashed blue line. Similarly, Fig. 13 reports the distribution for the last four cases reported in Table 6. The pure thermal operating points are depicted with light gray diamonds, the power-split points with dark gray squares and the battery charge points with black circles. In general, the battery charge is effective in moving the operating points of the engine toward the optimal operating line in terms of brake specific N[O.sub.x] emissions; the power split, instead, is used to move the engine operating points downward, in order to approach the optimal operating line in terms of brake specific N[O.sub.x] emissions. It can be seen in Fig. 12 that, since each case has also been optimized in terms of N[O.sub.x] emissions, the operating points that result from the control strategy optimization are predominantly distributed in the area that is not critical for N[O.sub.x] emissions, and that is still efficient in terms of fuel economy with respect to the optimal operating line. It is obvious that the engine is clearly oversized for most of the applications. The third and the fourth rows in Fig. 13 show how either the power-split or battery charge are employed to allow the engine to work predominantly around the blue optimal line, as both cases refer to the N[O.sub.x]-oriented optimization. Since the NOx emissions are extremely sensitive to any variation in the engine power, if the additional costs in terms of fuel and battery life consumption are not taken into account (as occurs for the NOx-oriented optimization), the control strategy selects the power flow that shifts the engine toward the blue line, in so far as this is compatible with the battery SOC constraint.

The results reported in Figs. 12 and J3 indicate that the results of the proposed CORE tool are similar to those of the benchmark optimizer, even in terms of control strategy, especially for the first four cases (i.e., the FC-N[O.sub.x]-BLC-oriented optimization).

Figure 14 reports the time histories of the battery SOC for the first four cases reported in Table 6, obtained with DP (solid blue line) and CORE (dashed red). Similarly, Fig. 15 reports the time histories for the last four cases.

First, it is interesting to observe that the N[O.sub.x]-oriented optimization (i.e., cases 7 and 8 in Table 6. which correspond to the third and fourth rows in Fig. 15) in general leads to a wider range of battery SOC than for the other cases. Second, the shape of the SOC time history obtained with CORE is similar to that obtained with DP, especially for the first four cases (i.e., the FC-N[O.sub.x]-BLC-oriented optimizations, see Fig. 14) For the last four cases (i.e., the FC-BLC and N[O.sub.x]-oriented optimizations, see Fig. 15). the use of the CORE tool in general leads to lower SOC time histories than the DP one, due to a higher battery usage and/or to a lower adoption of the battery charge working mode.

Figure 16 reports the control strategy that has been elaborated by the DP (left column) and the CORE (right column) tools for the first four cases reported in Table 6. in terms of power flow (see Table 2). Thirty clusters have been generated, in terms of vehicle velocity and power, according to the vehicle operating point distribution of the specific mission. A pie chart has been drawn for each cluster, in order to show the frequency distribution of the PF variable selected by the optimizer in the specific cluster. Each power flow value is associated to a sector of the circle, whose arc length is proportional to the frequency of that PF value. For example, let us consider the cluster at 30 km/h and 2.5 kW, in the bottom-left chart of Fig. 16. which is highlighted with a black circle. In this case, the frequency of the pure-electric torque-coupling (pe-tc, red sector) and the pure-thermal mode (pt-tc, dark green sector) is 40% each, while the pure-electric speed-coupling (pe-sc, yellow sector) makes up the remaining 20%. This graphical representation can be useful to compare the control strategy of different optimizers and to understand whether some rules are predominant for the different clusters.

Similarly, Fig. 17 reports the same graphical representation related to the last four cases reported in Table 6. It should be noted that the most frequently used control variable states are very similar for the benchmark (DP) and rule-based (CORE) optimizers. It is also straightforward to examine the frequency of the two pure-electric modes for the braking region, i.e. for negative power values. The figures may also be read in order to inspect whether a specific working mode has been selected and eventually in which cluster it might occur. For examples, it can be noted that the pe-sc, pe-tc and pt-tc modes are the most frequently selected strategies.

The CORE tool has been tuned and tested over the entire set of driving missions, for all the hybrid vehicles equipped with either the D1 or the D2 engine. The performance of the tool has been assessed with respect to that of DP for each mission, and a relative score has been assigned. The lower the score, the better the performance of the CORE tool. Figure 18 reports the score of the CORE tool for all the vehicles and driving missions, using the FC-N[O.sub.x]-BLC-oriented optimization. The average discrepancy of the CORE tool, with respect to DP, ranges from 0.8% for DMV-D1 up to 1.7% for SCVD2. As far as DMVs are concerned, the average discrepancy is 0.8% and 1% when using the D1 and D2 engines, respectively. It can also be noted that the standard deviation between the different missions is also very low, as it is of the order of 0.5% and 0.6% for the D1 and D2 engines, respectively. The worst performance occurs for SCV-D2 over the ARDC mission (2.6%). These results show that the CORE tool is extraordinarily capable of performing as well as the DP one, even though it is a rule-based optimizer. The main reason is due to the fact that the rule is extracted by means of a machine-learning technique, rather than being based on empirical rules driven by experience.

In addition to the results shown in Fig. 18, it is of fundamental importance to investigate the performance of the CORE tool over a specific driving mission [m.sub.1], after it has been tuned over a different driving mission [m.sub.2]. In this way, it is possible to estimate the effect of a cycle-dependent tuning of the tool and the additional improvements that might be achieved if the mission were known a-priori.

First, the CORE tool was tested over a mission [m.sub.1] of the [M.sub.1] set ([M.sub.1] = {NEDC, AUDC, ARDC, AMDC}) adopting the rule that has been extracted from the optimization process over an [m.sup.2] mission of the [M.sub.2] set ([M.sub.2] = {TC4, NEDC, AUDC, ARDC, AMDC}). The performance of the tool has been assessed with respect to that of the DP, and a relative score has been assigned for each mission. The lower the score, the better the performance of the tool. The discrepancy from DP has been averaged with respect to the [M.sub.2] set in order to analyze whether different types of rules could perform badly over a specific mission. The results are reported in the top section in Fig. 19. As an example, if the rules for SCV-D2 that have been extracted from the [M.sub.2] set are employed over NEDC, the average discrepancy is 12%. This evaluation method provides useful information about the deterioration of the CORE tool performance when the driving mission is not known a-priori, and to what extent a specific mission is affected by a non-specific tool calibration. An additional investigation on the tool robustness, in which the discrepancy from the benchmark optimizer has been averaged with respect to the [M.sub.1] set in order to analyze how a specific rule could perform over different types of missions, has been carried out. The results are reported in the bottom section of Fig. 19. For example, if the rule obtained over ARDC for DMV-D1 is applied over the entire [M.sub.1] set, the average discrepancy is only 1.05%. Similar results are obtained for DMV-D2, if the NEDC rule is selected. The rule extracted from NEDC seems to provide the least discrepancy with respect to the benchmark optimizer for all the hybrid architectures. However, if the rule extracted from AMDC for SCV-D2 is implemented over the cycles of the M2 set, the average discrepancy is 11.7%. This analysis provides useful information for a proper selection of the driving mission that should be used for the rule extraction when different hybrid architectures are considered.

Finally, the impact of the mesh size used for the definition of the clusters of the CORE tool (see Fig. 3) has been investigated, and the results are reported in Fig. 20 for DMV-D2, using the FC-N[O.sub.x]-BLC-oriented optimization. The first block is related to the results obtained with the tool, when a mesh of 8 * 8 * 2 = 128 clusters was created (8 vehicle velocity intervals, 8 velocity variation intervals and 2 battery SOC intervals). The second block is related to the tool with the default mesh (constituted by 9 * 9 * 3 = 243 clusters), while the third one refers to the tool with a mesh of 10 * 10 * 5 = 500 clusters. If the mesh dimension increases, the number of individuals and generations in the genetic algorithm solver, which is used to train the CORE tool, should also increase, and this would lead to an increase in the computational time required for the training. Moreover, if a too refined mesh is used, it is likely that a higher number of clusters will not intercept the actual vehicle operating conditions of the driving mission used to train the tool. It is worth recalling that the rule is identified by analyzing the results of the benchmark optimizer over the driving mission, and by selecting the most frequently adopted control strategy in the specific cluster. If the cluster does not intercept any real vehicle operating condition over the considered training mission, a backup rule is adopted, which is in general not optimal. The default mesh size (i.e., 243 clusters) has been selected as the optimal trade-off.

In short, it can be concluded that the performance of the CORE tool is almost equivalent to that of the benchmark optimizer, if a mission-dependent calibration of the tool is performed (see Fig. 11). However, even when the rule extraction is carried out on a different mission, the tool performance is still very good, provided the training mission is selected carefully (see the bottom charts in Fig. 19). The main reason for the good performance of the proposed tool is that the rule extraction is carried out using a machine-learning method, and is not based on empirical approaches driven by experience (as is frequently the case). In addition, the tool can easily be implemented in a vehicle control unit for a powerful fast real-time control strategy, as its application requires a very low computational effort, since the approach is of the rule-based type. In other words, the control unit has to compute, at a specific time instant, the 3D point that is associated to the current battery SOC, vehicle velocity and vehicle velocity variation (i.e., vehicle power demand). It then selects the parallelepiped that contains the point from the mesh of the available Nr parallelepipeds (see the scheme at the bottom in Fig. 3) The working mode is therefore easily read from the look-up table of rules, which had been previously stored in the control unit.

CONCLUSION AND FUTURE WORK

This present study has been focused on the development of a new machine-learning technique in order to develop a rule-based controller for the energy management of non-plug-in parallel hybrid electric vehicles that feature a torque-coupling (TC) device, a speed-coupling (SC) device or a dual-mode system, which is able to realize both the torque and speed coupling functions. The method has here been referred to as CORE (clustering optimization rule extraction). The performance of the proposed tool has been assessed over a set of different driving missions (NEDC, AUDC, ARDC, AMDC and TC4, i.e., an internally developed cycle) and compared with that of a global optimizer, which was used to identify the optimal control strategy. Moreover, the capability of the considered hybrid architectures to reduce fuel consumption and N[O.sub.x] emissions, in comparison with a conventional vehicle, has also been investigated. The simulated vehicles are equipped with compression ignition engines; two different engines, which are here referred to as D1 and D2, were considered; they are characterized by a displacement of 1.7L and 1.3 L, respectively, and by a brake power of 97 kW and 70 kW. The related data were provided by GMPT-E (General Motors PowerTrain-Europe). The main findings of this activity can be summarized as follows.

1. Performance of the considered hybrid architectures: it has been found that the vehicles equipped with the D2 engine are capable of reducing the overall costs (intended as the sum of the production costs and of the operating costs due to fuel consumption and battery depletion over a 250000 km mission) by 2.5%-5% with respect to the corresponding vehicles equipped with the Dl engine; the maximum cost reduction, with respect to the conventional vehicle, is obtained with DMV-D2 (17.7%). This layout is also characterized by a low payback distance, which can be of the order of 91 000 km over the TC4 mission. Moreover, it has been found that a control strategy optimization oriented toward reducing fuel consumption, battery depletion and N[O.sub.x] emissions at the same time, provides the best results.

2. Performance of the CORE tool: the performance of the proposed tool has been assessed with respect to that of the benchmark optimizer over different driving missions; it has been found that the accuracy of the CORE tool is almost equivalent to that of the benchmark optimizer, if a mission-dependent calibration is performed (average discrepancies of about 0.8% and 1% were found for the DMVs based on the Dl and D2 engines, respectively). However, even when rule extraction is carried out on a different mission, the tool performance is still very good, provided a proper training mission is selected. For example, if the tool training is performed over NEDC, and the extracted rule is applied to the other missions, the discrepancies, with respect to the benchmark optimizer, range from 0.1 to 2.7 %. The main reason for the good performance of the proposed tool is that the rule extraction is carried out using a machine-learning method, and is not based on empirical approaches driven by experience, as is frequently the case. Moreover, the tool can easily be implemented in a vehicle control unit for a powerful fast real-time control strategy, as its application requires a very low computational effort, since the approach is of the rule-based type.

Some topics and ideas have emerged from this study and they will be investigated in detail in the near future. For example, a new algorithm that also takes into account data from the network and the infrastructure is currently under investigation; this would allow the best tuning to be selected for the CORE tool, according to the type of mission the driver is about to tackle. Moreover, the performance of the tool will also be investigated considering hybrid architectures equipped with spark-ignited engines.

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CONTACT INFORMATION

Ezio Spessa (Associate Professor)

IC Engines Advanced Laboratory

Dipartimento Energia, Politecnico di Torino

c.so Duca degli Abruzzi, 24 - 10129 Torino (Italy)

phone:+39-011-090.4482

ezio.spessa@olito.it

ACKNOWLEDGMENTS

GMPT-E is acknowledged for the technical support in the activities.

DEFINITIONS/ABBREVIATIONS

AMDC - Artemis Motorway Driving Cycle

ARDC - Artemis Road Driving Cycle

AUDC - Artemis Urban Driving Cycle

be - Battery charge

BEV - Battery Electric Vehicle

[C.sub.bat] - Battery capacity

CM - Configuration Matrix

CORE - Cluster Optimization Rule Extraction

[C.sub.pt] - Powertrain configuration

[C.sub.pt\bat] Powertrain configuration for the CM approach

DMV - Dual-Mode Vehicle

DP - Dynamic Programming

Dl - 1.7 L Euro 5 GM prototype diesel engine

D2 - 1.3 L Euro 5 GM prototype diesel engine

E - Engine

EM - Electric Machine

ES - Engine State

FC - Fuel Consumption

FD - Final Drive

GA - Genetic Algorithm

GB - Gear Box

GM - General Motors

GN - Gear Number

HEV - Hybrid Electric Vehicle

[I.sub.bat] - Battery current

J - Objective function

NEDC - New European Driving Cycle

[N.sub.in] - Number of time intervals

pe - Pure electric

PF - Power Flow

[P.sub.fd] - Final drive power

PG - Planetary Gear

ps - Power split

pt - Pure thermal

[P.sub.v] - Vehicle power

[R.sub.wh] . - Wheel radius

SC - Speed Coupling

SCV - Speed Coupling Vehicle

[S.sub.es] - Set of discrete values of the state of the engine

[S.sub.gn] - Set of discrete values of GN

SOC-State of charge

[S.sub.pf] - Set of discrete values of PF

[S.sub.soc] - Set of discrete values of SOC

t - Time

TC - Torque Coupling

TCV - Torque Coupling Vehicle

TC4 - Internally-developed Test Cycle

TR - Transmission

u - Control strategy

[V.sub.v] - Vehicle velocity

GREEK SYMBOLS

[alpha] - Sub-control variable of PF

[lambda] - Battery life consumption

[[lambda].sub.r] - Residual battery life consumption

[LAMBDA] - Battery life duration

[sigma] - Severity factor

[TAU] - Speed ratio of the transmission

[[tau].sub.tc] - Speed ratio of the torque-coupling device (GB)

[[TAU].sub.SC] - Speed ratio of the speed-coupling device (PG)

Roberto Finesso, Ezio Spessa, and Mattia Venditti

Politecnico di Torino

Table 1. Transmission speed ratio specifications.

GN        1     2     3     4     5     6

[tau][-]  4.17  2.13  1.32  0.95  0.75  0.62

Table 2. Working modes of the Dual-mode vehicle.

   PF     [alpha]  [[omega].sub.e]   [[omega].sub.em]     [P.sub.e]

1  pe.tc   1       0                 [[omega].sub.era,t]  0
2  pe.se   1       0                 [[omega].sub.em,s]   0
3  pt.tc   0       [[omega].sub.et]   0                   [P.sub.f]
4  ps.tc   1/2     [[omega].sub.et]  [[omega].sub.em,t]   [P.sub.e]
5  bc.tc  -1/2     [[omega].sub.et]  [[omega].sub.em,t]   [P.sub.e]
6  ps.se   1/2     [[omega].sub.es]  [[omega].sub.em,s]   [P.sub.e]
7  bc.se  -1/2     [[omega].sub.es]  [[omega].sub.em,s]   [P.sub.e]

   PF     [P.sub.em]

1  pe.tc  [P.sub.f]
2  pe.se  [P.sub.f]
3  pt.tc  0
4  ps.tc  [P.sub.em]
5  bc.tc  [P.sub.em]
6  ps.se  [P.sub.em]
7  bc.se  [P.sub.em]

Table 3. Values of the main parameters of the genetic algorithm.

Population dimension           [N.sub.ind]      2000
Generation                     [N.sub.g]          30
Crossover factor               [chi]               0.75
Normalized mutation amplitude  [[micro].sub.0]     1
Fraction of mutated genome     [[micro].sub.1]     0.1

Table 4. Main specifications of the set of driving cycles.

                       TC4     NEDC     AUDC    ARDC     AMDC

T [min]                171     1179     993     1080     1068
D [km]                   2.76    10.93    4.86    17.27    29.53
[bar.V.sub.v] [km/h]    58       33.4    17.6     57.6     99.5
[bar.V.sub.v]' [km/h]   58       42.4    22.5     58.2    100.7
[V.sub.v.max] [km/h]   108      120      57.2    111.5    148.3
[P.sub.tr,max] [kW]     40.5     32.6    27       42.7     49.3
[P.sub.br.max] [kW]    -51.5    -27.3   -40.4    -62.9    -81.5
[bar.P.sub.tr] [kW]     11.6      6.5     6.8     10       20.6
[bar.P.sub.br] [kW]    -11.1     -5.7    -4.5     -7.4    -13.1
[E.sub.tr] [kWh]         0.4      1.23    0.74     2.06     5.01
[E.sub.br] [kWh]        -0.15    -0.38   -0.48    -0.67    -0.67

Table 5. Specifications of the components of the hybrid vehicles.

         ENGINE  BATTERY  EM    TC    SC   FD

D1  TCV  100     30       30    0.59       3.25
    SCV  100     32.5     32.5        2.7  2.5
    DMV  100     27.5     27.5  0.5   4.5  2.5
D2  TCV   70     42.5     42.5  0.91       3.25
    SCV   70     50       50          2.7  2.5
    DMV   70     40       40    0.5   4.5  2.5

Table 6. Investigated cases for the analysis of the effect of different
oriented optimizations for DMV.

Case  Engine  Mission  Optimization

1     Dl      NEDC     FC-NOx-BLC
2     D2      NEDC     FC-NOx-BLC
3     Dl      AUDC     FC-NOx-BLC
4     D2      AUDC     FC-NOx-BLC
5     D2      NEDC     FC-BLC
6     D2      AUDC     FC-BLC
7     D2      NEDC     N[O.sub.x]
8     D2      AUDC     N[O.sub.x]
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Title Annotation:hybrid electric vehicle
Author:Finesso, Roberto; Spessa, Ezio; Venditti, Mattia; di Torino, Politecnico
Publication:SAE International Journal of Alternative Powertrains
Article Type:Report
Date:Jul 1, 2016
Words:15115
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