Simulation-based optimal design of heavy trucks by model-based decomposition: an extensive...

Int. J. of Heavy Vehicle Systems, Vol. 11, Nos 3/4, 2004 403

Simulation-based optimal design of heavy trucks by model-based decomposition: An extensive analytical target cascading case study

M. Kokkolaras, L.S. Louca, G.J. Delagrammatikas, N.F. Michelena*, Z.S. Filipi, P.Y. Papalambros, J.L. Stein and D.N. Assanis Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA

Email: [email protected]

Abstract: We present the findings of an extensive case study for the decomposed, simulation-based, optimal design of an advanced technology heavy truck by means of analytical target cascading. The use of a series hybrid-electric propulsion system, in-hub motors, and variable height suspensions is considered with the intention of improving both commercial and military design attributes according to a dual-use philosophy. Emphasis is given to fuel economy, ride, and mobility characteristics. The latter are predicted by appropriately developed analytical and simulation models. This article builds on previous work and focuses on recent efforts to refine the applied methodologies and draw final conclusions.

Keywords: analytical target cascading, heavy truck, hierarchical decomposition, hybrid-electric powertrain, optimal vehicle design, simulation-based analysis.

Reference to this paper should be made as follows: Kokkolaras, M., Louca, L.S., Delagrammatikas, G.J., Michelena, N.F., Filipi, Z.S., Papalambros, P.Y., Stein, J.L. and Assanis, D.N. (2004) ‘Simulation-based optimal design of heavy trucks by model-based decomposition: An extensive analytical target cascading case study’, Int. J. of Heavy Vehicle Systems, Vol. 11, Nos 3/4, pp. 403–433.

* Dr Nestor Michelena passed away on December 22, 2002, following a long illness. He remained strongly involved in this research and was an inspiration to all of his colleagues. He is sorely missed.

1 Introduction

Optimal design of a large and complex vehicle such as a truck can only be accomplished by decomposition. In simulation-based design, this decomposition is dictated by the availability of models. In most cases, model-based decomposition results in a hierarchical

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404 M. Kokkolaras et al.

structure: the vehicle is decomposed into systems, the systems into subsystems, the subsystems into components, and so on.

Analytical target cascading (ATC) (Kim, 2001) is a methodology developed for use during the early development phase of large and complex systems to propagate desirable overall product targets to appropriate individual specifications for the various subsystems and components in a consistent and efficient manner. Consistency requires that all parts of the optimally designed system should work well together. Efficiency aims at reducing/avoiding design iterations at later stages, which are costly in time and resources.

ATC is implemented as a multilevel optimal design problem. Design targets are cascaded to lower levels using the model-based, hierarchical decomposition of the design problem. An optimisation problem is posed and solved for each design subproblem to minimise deviations from propagated targets. Solving the subproblems according to an appropriate coordination strategy yields overall system compatibility. ATC is compared to other hierarchical formulations for design by decomposition in Kim (2001). Convergence properties of ATC are discussed in Michelena et al. (2002).

The ATC methodology has been applied to the optimal design of an advanced technology heavy truck during an extensive case study. The initial concept considered two alternatives for the propulsion system (electric and series hybrid-electric), in-hub motors, and variable height suspensions for the design of the truck with the intention of improving both civilian and military design attributes according to a dual-use philosophy (Michelena et al., 2001). Emphasis was given to fuel economy, ride quality, and mobility characteristics. Simulation and analytical models were developed to simulate the transient response of the truck and the response of variable height suspensions at the top (vehicle) and bottom (system) levels, respectively. A bi-level target cascading hierarchy was defined according to the availability of the models. Baseline designs were chosen to be comparable to existing trucks of the US Army. Design Targets were defined to improve fuel efficiency while maintaining performance characteristics relative to those of the existing conventional heavy trucks. Only lead-acid batteries were considered for the hybrid-electric propulsion system.

The engine was later included at the system level by introducing an appropriate simulation model so that design targets could also be translated to engine specifications (Louca et al., 2002). Moreover, additional battery types were considered to study their effect on fuel economy. The optimal design problem was reformulated to reduce the number of design targets and increase trade-off visualisations. A more aggressive driving schedule was used to assess performance constraints, ride quality, and regenerative braking benefits. The location and suspension characteristics of the driver’s seat were included as design variables at the vehicle level. Finally, based on the observations made during the initial phase of the case study, only the series hybrid-electric propulsion system was considered.

In this article we employ a composite optimisation technique, i.e. mixed use of gradient-based and derivative-free algorithms, to avoid the shortcomings encountered when using gradient-based algorithms in simulation-based design optimisation, i.e. convergence to local optima. In addition, the number of design variables is reduced to include only those proven to be significant with respect to the design attributes: we omit design variables related to the driver’s seat, and consider suspension characteristics of the front and rear axle pairs to be identical.

It is emphasised that the scope of this paper is to demonstrate the application of the ATC process by means of a case study. Theoretical issues of the ATC process or

Optimal design of heavy trucks by model-based decomposition 405

decomposition approaches are not discussed. As indicated by the title, the decomposition is driven by the availability of analysis/simulation models.

The article is organised as follows. The ATC formulation for vehicle design is presented in the next section. The necessary simulation models are described in detail in sections 3 and 4. The case study is reviewed in Section 5, and the latest results, based on extensions and modifications described in Section 6, are presented in Section 7. Finally, conclusions are drawn in Section 8.

2 Target cascading for vehicle design

The mathematical formulation of the analytical target cascading process is presented using general notation, from which the optimal design problem for each element (i.e. vehicle, system, subsystem, or component) can be recovered as a special case. Two types of responses, and , are associated with ‘local’ targets (e.g. at the top level) and ‘cascaded’ specifications, respectively. The latter link two successive levels in the problem hierarchy. The design problem P

R R̂

ij corresponding to the j-th element at the i-th level is formulated as follows.

( ) ( )

( ) ( )

( ) ( )( )( ) ( )( )

1

1

1 1

1 1

1 ,..., 1 ,

1 ,..., 1 ,

ˆmin

subject to

g ,

h ,

ij

ij

ij

cij

cij

U U Rij ij ij ij ij ij ij ij

x

L Riji k i k

k C

Liji k i k

k C

ij ij iji k i k

ij ij iji k i k

ε

ε

0,

0,

y

y

ε ε

ε

ε

+ +

+ +

+ +

+ +

− + − + − +

− ≤

− ≤

≤

=

∑

∑

R T R R y y

R R

y y

R R x y

R R x y

(1)

where with (·)( ) ( )( 11 ,..., 1ˆ, r , ,

ij

tt tij ij ij ij c ij iji k i k+ +

= = R R R R R x y

{ }1,...ijck

) t denoting transpose,

is the set of children of element j at level i, and cijC k= ij is the number of

children. Note that an element’s responses depend on the element’s design variables as well as on its children’s responses. In the above problem formulation,

• ( ) ( ) ( ) ( )1 11 1 1 1, , ,..., , , , ,c cij ij

tt t t t t t R y

ij ij ij ij iji k i k i k i k ε ε+ + + + =

x x y y y R R… is the vector of all

optimisation variables,

• xij is the vector of local design variables, that is, variables exclusively associated with the element,

• yij is the vector of linking design variables, that is, variables associated with two or more elements that share the same parent,

• Rij is the vector of all responses,


• Rijε is the tolerance optimisation variable for coordinating the linking design

responses of the children of the element,

• yijε is the tolerance optimisation variable for coordinating the linking design

variables of the children of the element,

• Tij is the vector of local target values,

• is the vector of response values cascaded down to the element from its

parent,

UijR

• Uijy is the vector of linking design variable values cascaded down to the element

from its parents,

• is the vector of response values cascaded up to the element from its k-th

child, ( )1Li k+R

• is the vector of linking design variable values cascaded up to the element

from its k-th child, ( )1Li k+y

• gij and hij are vector functions representing inequality and equality design constraints, respectively,

• ⋅ denotes some metric for evaluating deviations; typically, the square of a weighted norm is used for the metrics involving local targets Tij to facilitate tradeoff evaluation studies, while the square of the l2-norm is used in all other cases.

The information flow of updated parameters before (input) and after (output) solving the optimisation problem at each element of the hierarchy is illustrated in Figure 1.

The ATC process is based on the model-based, hierarchical decomposition of the original optimal design problem. It is emphasised that analysis/simulation models are necessary to compute the responses of all the elements that comprise the system. Typically, the level of abstraction and fidelity in these models increases as more levels are introduced in the hierarchy, since further decompositions require more detailed element representation. For this case study, a bi-level hierarchy has been defined based on the developed simulation and analytical models. The truck is represented at the top (vehicle) level; the engine and the two (front and rear) suspensions are represented at the bottom (system) level. Local design targets are defined only at the vehicle level. Although it is possible to assign weights to different targets to express preferences of satisfying one target over another, we do not consider this option in this paper. We do, however, consider the possibility of defining different sets of target values, which can be viewed as a way to assign weights. Note that there are no linking variables in this hierarchy, i.e. none of the system-level problems share a design variable. The formulation of the optimal design problems in this bi-level hierarchy is presented in the next two sections.


Figure 1 Information flow to and from each element optimisation problem.

2.1 Vehicle-level design problem

At the vehicle level, responses Rv must match design targets Tv. These responses are functions of vehicle design variables xv and system responses Re, Rfs, and Rrs of the engine, front suspension, and rear suspension, respectively, i.e. Rv = rv(xv, Re, Rfs, Rrs). System responses Re, Rfs, and Rrs and vehicle design variables xv are determined by solving an optimisation problem formulated as

( )

x , , , ,min

subject to

, x 0,

Rv e fs rs v

Rv v v

L L Le e fs fs rs rs v

v v v

ε

R

ε

ε

− +

− + − + − ≤

≤

R R RR T

R R R R R R

g R

(2)

where Rvε is a tolerance variable for coordinating system responses, , L

eR LfsR , and

are system response values passed up to the vehicle from the engine, front suspension, and rear suspension systems, respectively, and g

LrsR

v is a vector of functions representing the vehicle design constraints. Note that there are no equality constraints.

2.2 System-level design problem

Once the optimal values of the system level responses Re, Rfs, and Rrs are determined by solving the vehicle-level design problem, they are cascaded down to the system level as


parameters , UeR U

fsR , and , respectively. At the system level, three individual

minimum deviation optimisation problems are formulated to determine the system design variables x

UrsR

e, xfs, and xrs of the engine, the front suspension, and the rear suspension, respectively. System responses are functions of system design variables, i.e. Ri = ri(xi), for i {e,fs,rs}. Each of the three optimisation problems at the system level is formulated as

∈

( )

min

subject to , 0,i

Ui ix

i i i

−

≤

R R

g R x (3)

where i ∈ {e,fs,rs} denotes the system related to the engine, the front suspension, and the rear suspension.

The responses Ri, i ∈ {e,fs,rs}, are passed up to the vehicle-level problem as parameters after solving the three system-level problems. L

iR

3 Vehicle-level modelling

The ATC process is applied to a concept design of a heavy truck that features advanced technology systems aimed at improving the performance of its predecessor under similar operating conditions. Fuel economy, mobility, and ride quality are the critical attributes that the new design must improve or maintain. The design process begins with identifying the key technologies that are expected to have the highest impact on the improvement of these attributes. This is an exploratory study, based on abstract information provided by manufacturers and research results, which generates alternative designs for future analysis. The next step is to evaluate the proposed designs using detailed modelling and simulation. This task can be performed efficiently using ATC, where system specifications are determined to meet fuel economy, mobility, and ride quality targets. The truck concept chosen for the case study is shown in Figure 2.

Figure 2 Truck design concept.


The concept vehicle has a series hybrid-electric configuration with in-hub motors at

all eight wheels. Figure 3 is a schematic of the vehicle configuration. The truck is powered by an advanced diesel engine that is connected to the generator using a gearbox. The electric power of the generator is delivered through the power bus to the in-hub motors that drive the wheels after a speed reduction. Additional power may be supplied by the batteries upon vehicle demand. A control module manages the distribution of power and the charging or discharging of the batteries based on instantaneous power requirements. A new technology also utilised here is the trailing arm suspension, which provides high ground clearance for off-road driving conditions and low overall height for air transport, via its variable height capability.

Figure 3 Vehicle model configuration.

An integrated truck model is developed for vehicle-level analysis during the ATC process. Given that the design targets at the vehicle level are fuel economy, mobility, and ride quality, an appropriate model is generated that predicts vehicle responses associated with these quantities accurately and efficiently. The integrated model is based on the Vehicle-Engine SIMulation (VESIM), a modelling and simulation environment that provides a system library for straightforward generation of vehicle models (Assanis et al., 2000). This library includes electric components for modelling electric or hybrid-electric powertrains (Lin et al., 2001). The first VESIM models were configured in Matlab/Simulink for conventional and hybrid-electric vehicles, and have been utilised to assess the ability of advanced power management strategies to improve the fuel economy potential of a parallel hybrid-electric truck (Lin et al., 2001). Although previous experience with hybrid-electric system simulation provided a good foundation for the current work, constructing a series hybrid-electric propulsion system with eight in-hub motors required significant modifications to the system architecture. These enhancements included larger, updated components and a refined power management strategy. In addition, the prospect of using the vehicle simulation within the ATC optimisation framework motivated its implementation in a more computationally efficient modelling


environment. Furthermore, the vehicle model’s complexity necessitated the use of decomposition and hierarchical modelling.

At the top level of the hierarchy, the VESIM model consists of the engine, drivetrain (batteries, motors, generator, and power bus), vehicle dynamics, driver, and hybrid control modules, as shown in Figure 4. A feed-forward simulation scheme is selected to enable studies of control strategies under realistic transient conditions. The first source of excitation comes from the driver, who controls the vehicle’s forward speed by means of the fuel and brake pedals. The driver’s command is translated by the hybrid controller into signals defining the operation of the diesel engine, generator, and in-hub motors. The vehicle is constrained to move only in the pitch plane and has three degrees of freedom (longitudinal, heave, and pitch). This model is sufficient since there is no steering input to induce yaw or roll motion. The next excitation comes from the road that is generally uneven and imposes a vertical velocity to the tyres. Road excitation is applied to the four sets of tyres as a function of their longitudinal position. Note that the vehicle-level model resembles the vehicle’s actual configuration. In contrast to previous efforts that relied on Simulink, the integrated vehicle model was developed using the 20SIM (2001) modelling and simulation environment (Louca et al., 2001). The latter supports hierarchical structuring and allows physical modelling by means of bond graphs (Rosenberg and Karnopp, 1983; Karnopp, et al., 1990), block diagrams, or direct equation formulation. In addition, 20SIM allows the generation of stand-along code that is quite efficient for multiple evaluations of vehicle performance during the ATC process.

Figure 4 Vehicle model VESIM as implemented in 20SIM.

The model-based hierarchy of the case study is illustrated in Figure 5. The necessary simulations are performed by the VESIM model at the vehicle level and the diesel engine, rear suspension, and front suspension models at the system level. The vehicle-level model predicts the vehicle responses required by the corresponding optimisation problem. At the system level, the diesel engine model predicts the engine map and


fuelling curve, while the trailing arm model predicts the compliance and damping for both the rear and front suspensions.

Figure 5 Model hierarchy.

3.1 Engine

High-fidelity thermodynamic models of in-cylinder processes and engine components have been used to study powertrain transient response during vehicle acceleration (Assanis et al., 2000). Alternatively, a simplified but more computationally efficient engine module utilising torque look-up tables has been developed for system-level studies (Lin et al., 2001). The latter approach is selected for this study since multiple simulation runs are needed during the optimisation process, each being performed over a relatively long driving schedule. However, previous experience with high-fidelity modelling is used to add important features to the engine module’s look-up table, in order to improve its dynamic response. Although the objectives of this study require the use of a simple engine module, it is deemed necessary to retain features critical for transient response. Namely, the engine model has to incorporate a realistic fuel injection control module and include a delay function in the fuel injection controller to effectively simulate the lag associated with the turbocharger’s response delay and limited fuelling. Hence, the VESIM engine module is composed of two main parts: the torque map look-up table and the fuel controller, as shown in Figure 6. This module is supplemented with engine inertia, which is not shown in the figure since it is lumped with the generator inertia to avoid computational difficulties.

Engine maps are look-up tables obtained from actual engine measurements, typically torque readings for specific speed-fuel combinations. Alternatively, these look-up tables can be generated from high fidelity in-cylinder and engine component models. However, the design optimisation problem cannot be solved within a reasonable amount of time when using such computationally intense simulation models. Therefore, we developed a


surrogate model of the engine submodel to reduce computational cost. Representative engine characteristics were used to generate a number of corresponding torque maps and maximum fuelling rate curves. These data were generated using the Turbocharged Diesel Engine Simulation (TDES), described in Section 4.2, and used to train two artificial neural networks (ANN). A similar procedure was successfully implemented in Kim et al. (2002).

Figure 6 Engine submodel in 20SIM.

Table 1 Range of engine characteristics for Latin hybercube design of experiments.

Characteristic Minimum Maximum

Displacement [l] 9.5 16.0 Compression ratio [-] 12 22 Maximum boost pressure [atm] 2 3 Wastegate activation point [rpm] 1420 2250 Injection timing [oATDC] 335 355

A Latin hypercube design of experiments (DoE) was used to sample the design space

defined by the following five input variables: engine displacement, compression ratio, maximum boost pressure at maximum speed, wastegate activation point, and injection timing as input parameters. The engine parameter ranges are given in Table 1. Two different Latin hypercubes were generated, whose points were used as input to compute the necessary output for training two different radial basis function artificial neural networks; 150 such input-output relations were used for the torque map network and 300 input-output relations were used for the maximum fuelling rate curve. The training


procedure is illustrated in Figure 7. Cross-validation error studies yielded less than 5 per cent average relative errors for both networks.

Unlike the procedure described in Kim et al. (2002), the engine design generated by the neural network is optimised with respect to injection timing throughout its operating regime. This ‘internal’ optimisation procedure is summarised as follows (Delagrammatikas and Assanis, 2001). The current engine design, as specified by the first four input variables of Table 1, is used to calculate a torque map for each injection timing between 335 and 355 degrees after top dead centre (ATDC) with a one degree increment. For every speed-fuel combination, the maximum torque found among the maps is selected. The resulting map is used as the engine torque map at the vehicle level. The corresponding injection timings are stored as an injection timing control map that can be useful to injection system designers at the system level.

Figure 7 Artificial neural network training procedure.

3.2 Drivetrain

The drivetrain submodel consists of the generator and its gearbox, power bus, four sets of in-hub motors with a gearbox, and batteries as depicted in Figure 8. The drivetrain provides the connection between the engine and the vehicle dynamics. The generator gearbox input shaft and in-hub motor gearboxes are the connecting points for the engine and vehicle dynamics models, respectively. The inputs are defined by the engine torque and rotational speed for each wheel, and the outputs are given by the torque to each wheel, the generator rotational speed, and the battery power. The in-hub motors, generator, and batteries are connected to the power bus that controls the power flow


between these electrical components. The power flow is controlled by the power control signal, as discussed in Section 3.4. The power bus is assumed ideal (no energy losses).

Figure 8 Drivetrain configuration.

3.2.1 Motors and generator

The motor model is taken from the ADVISOR library (Brooker et al., 2000) and is depicted in Figure 9. Motor dynamics are approximated by a first-order lag. Motor torque output is limited due to the maximum battery power and motor torque limits. An 83-kW AC-induction motor is selected as the baseline electric motor. Efficiency is a function of motor toque and speed. A similar model is used for the generator that is connected to the diesel engine via a speed reduction gearbox to transform mechanical into electrical power. The engine and generator combination is referred to as power generating unit (PGU). A 350-kW generator is matched with the baseline diesel engine. Generator inertia is combined with engine inertia to solve PGU dynamics. Both engine and generator efficiency are considered when optimising PGU operation, as described in Section 3.4. The motor and generator torques are scaled linearly during the optimisation process to determine their optimal sizes.

3.2.2 Batteries

The batteries submodel uses an electrical equivalent circuit to predict battery performance (Michelena et al., 2001). The effects of using different battery types on fuel economy and performance are studied by using Lead-Acid (Pb), Lithium-Ion (Li), and Nickel Metal-Hydride (NiMH) battery modules. Module mass and energy for each battery type are given in Table 2. Open circuit voltage and charging and discharging resistance data, taken from the ADVISOR library (Brooker et al., 2000), are illustrated in Figure 10. Different charging and discharging resistance behaviour are expected to affect the optimal values of minimum and maximum state of charge limits (SOC) and the charging point. Note that battery power can be increased by increasing the number of


battery modules. The associated increased weight is included in the model even though it has a negligible effect on fuel efficiency and performance due to the relatively large weight of the truck. However, packaging considerations are not taken into account in the model.

Figure 9 AC induction motor model.

Figure 10 Voltage and charging and discharging resistance data.


3.3 Vehicle dynamics

The vehicle dynamics module considers the vehicle’s wheels, tyres, axles, suspensions, and body. The vehicle is modelled as a collection of rigid bodies that are allowed to move in the two-dimensional space subject to forces, moments, and rigid constraints (see Figure 11). Forces and moments are physical elements that act at specific points between two bodies (e.g. the suspension force between the wheel hub S2 and the attachment point on the body P2). In addition, two bodies can be restrained to move in a specific trajectory by a rigid constraint (e.g. the front axle is constrained to move perpendicular to the body, i.e. along the y-axis).

Figure 11 Pitch plane dynamics schematic.

The body is modelled as a rigid body that is free to pitch and move horizontally and vertically. Here inertial elements are used to represent the dynamics in three degrees of freedom. The kinematics are described in a body-fixed coordinate systems (x, y), and represented by the nonlinear Euler equations. The body includes four points (P1, P2, P3, P4) for connecting the axles at fixed locations relative to the CG. Finally, aerodynamic drag is modelled by energy losses that are quadratic with forward vehicle velocity.

Each axle is modelled as a rigid body with its kinematics described in a body-fixed coordinate system (xsi, ysi) (see Figure 11). A rigid constraint is placed on the axle which moves on an axis with its origin at the attachment point (Pi), perpendicular to the horizontal axis of the frame (xi, yi), where i = 1,2,3,4 denotes each of the four axles. The axle is also constrained by the suspension that is modelled as a linear spring and damper connected in parallel. Finally, the unsprung mass gravity force is applied to the axle through a transformation of local velocities into the global frame (X,Y).

The tyre submodel includes wheel dynamics and tyre-road interaction. Wheel mass is lumped to the axle to avoid additional kinematic constraints and computational inefficiencies. The model includes the wheel moment of inertia and bearing viscous


losses at the wheel hub. Drive torque from the electric motor is applied to the hub to accelerate the wheel. A simple brake model with Coulomb and viscous friction is included to generate the required torque for decelerating the vehicle. Tyre rolling resistance is included in the model as an additional energy loss term.

Tyre forces in the vertical direction are modelled as a linear spring and damper connected in parallel. The model can also predict wheel lift off. The longitudinal traction force is calculated using the Pacejka model (Pacejka and Bakker, 1993). First, the axle velocity at point (Si) is converted in a frame that is aligned with the road at th contact point. This coordinate transformation gives the forward velocities of the contact point (in the (xri, yri) frame) that is used to calculate wheel slip. Finally, the traction force is calculated as a nonlinear function of wheel slip and normal load. The constants in the Pacejka model are estimated from measured data of the actual tyre.

3.4 Power management

The power management strategy is based on engineering intuition and straightforward analysis of component efficiencies (Lin et al., 2001; Anderson and Pettit, 1995). The power management process starts by interpreting the driver pedal signal as a power request Preq. According to this power request, the operation of this controller is divided into three control modes: braking, normal and recharging. In the event of a negative power request, the braking mode is engaged to decelerate the vehicle. If the power request is positive, either the normal or recharging mode is used according to a charge-sustaining policy. This strategy assures that the battery state of charge (SOC) remains within predefined lower and upper bounds, for efficient operation and depletion/damage prevention. Under normal propulsive driving conditions, the normal model control determines the power flow in the series hybrid drivetrain. Whenever the SOC drops below the lower limit, the controller will temporarily switch to the recharging mode until the SOC reaches the upper limit; normal mode operation resumes thereafter. The basic logic of each control mode is briefly described below.

3.4.1 Normal mode

The battery is the prime power source in this mode. The PGU (engine and generator) is shut off and the battery supplies the requested power to the electric in-hub motor. However, once the power request exceeds battery output ability, the engine is activated to supplement power demand. PGU power is given by the following equation:

0 if

ifreq bat

PGUreq bat req bat

P PP

P P P P

<= − ≥ (4)

3.4.2 Charging mode

The PGU is the prime power source in this mode. In addition to powering the electric motor, the PGU has to provide additional power to charge the battery. A constant recharge power level is added to the PGU’s power request.


max min

max min

if

ifreq

PGUreq bat

P SOC SOC SOCP

P P SOC SOCα

> >= + ≤ (5)

where α is the fraction of the charging power limit, and SOCmin and SOCmax denote minimum and maximum allowed state of charge, respectively. The battery power command becomes negative to recharge the battery. One exception is when the total power request is greater than the maximum PGU power, in which case the battery will assist the PGU to power the electric motors. Once the PGU power request is determined, the desired engine torque and speed can be found from the curve shown in Figure 12. This curve is calculated by combining engine and generator efficiencies, and represents the most efficient operating points for each engine power level.

Figure 12 Best PGU efficiency curve.

3.4.3 Braking mode

Brake pedal actuation is interpreted as a negative power request. Regenerative braking is activated to absorb braking power. However, when the braking power request exceeds the regenerative braking capacity, due to battery or motor limits, friction braking is used to produce the required vehicle deceleration.

Due to the large mass of trucks, regeneration is critically important for realising fuel economy benefits when hybridising heavy vehicles (Wu et al., 2002). Illustrations of energy flow through the hybrid system during driving conditions initiating regeneration events can be found in (Wu et al., 2002; Lin et al., 2001).


Figure 13 Trailing arm suspension.

4 System-level modelling

4.1 Suspension

A detailed model of the suspension is needed to predict the equivalent stiffness and damping parameters that are passed from the lower to the upper design levels in the ATC hierarchy. The suspension’s trailing arm houses two hydraulic chambers (C1 and C2) and a pneumatic chamber (C3), as shown in Figure 13. The arm’s swinging motion about its pivot (point O) moves the piston that compresses the fluid in chamber C3 after the hydraulic fluid is forced to pass through the orifice. This mechanism provides the stiffness characteristics, while the fluid flow through the orifice of area A12 provides viscous and hysteretic energy losses. Stiffness and damping characteristics are calculated using the nonlinear kinematics of the trailing arm, which depend on the geometry and fluid properties. Quantities treated as optimisation variables in the system-level design problem include the high-pressure piston area AS, the lower-pressure piston area AP, the orifice area A12, the wheel hub location LH, the rod hitch point coordinates (X3, Y3), the rod length LR, and the trailing angle α.


Figure 14 Schematic of complete TDES system.

4.2 Engine

The Turbocharged Diesel Engine Simulation (TDES) used in this work is a modified version of the FORTRAN-based code first developed by Assanis and Heywood (1986). TDES is a zero-dimensional, quasi-steady, feed-forward engine simulation that predicts engine outputs at a single operating point (engine speed and duelling rate combination). The diesel four-stroke cycle is treated as a sequence of continuous processes: intake, compression, combustion (including expansion), and exhaust. Quasi-steady, adiabatic, one-dimensional flow equations predict mass flows past the intake and exhaust valves. Combustion is modelled as a uniformly-distributed heat release process, using Watson’s correlation (1980). Convective heat transfer in the combustion chamber is modelled using a Nusselt number correlation based on turbulent flow in pipes and the characteristic velocity concept for evaluating the turbulent Reynolds number (Tennekes and Lumley, 1972). The characteristic velocity and length scales required by these correlations are obtained from an ‘energy cascade’ zero-dimensional turbulence model (Heywood, 1988). Radiative heat transfer is added during combustion. A friction sub-model based on the Millington/Hartles correlation is used to predict the engine friction losses and convert indicated to brake quantities (Millington and Hartles, 1968). To complete the system, the fundamental equations for turbocharger design, found in Watson and Janota (Watson and Janota, 1982), were implemented in conjunction with a simplified wastegate model. A schematic of the overall system is shown in Figure 14. These relations were incorporated into a parameterisation scheme modelling the inlet boost profile throughout the engine’s


operating regime (Delagrammatikas, 2001). The exhaust manifold back-pressure was subsequently back-calculated from fundamental principles. This scheme is illustrated in Figure 15. In so doing, only three parameters were used to define the inlet boost: PIMmax (maximum attainable inlet boost pressure), WRPM (wastegate activation point), the PIMmid (inlet boost pressure at wastegate activation point). Note that PIMmax is required to be greater or equal than PIMmid.

Figure 15 Parameterisation scheme used in TDES to model inlet boost profile.

The vehicle model requires a maximum fuelling curve and an engine map from TDES. A modified Newton-Raphson technique was developed to first calculate the engine’s maximum torque curve (Delagrammatikas and Assanis, 2001). Next, the fuelling rates from this step were used to define the fuel axis limits on the engine map (the maximum fuelling rate was used as the axis’ upper bound while 25 per cent of the minimum was used as the lower bound). The speed range was predefined, as were the number of increments for each axis. Finally, the speed/fuel combinations on each map point were visited by TDES, using the corresponding, fuel-weighted, inlet boost pressure to calculate output torque. All map points were populated with TDES data except for those located above the maximum fuelling curve. The engine would never operate in these regimes. Therefore, the unnecessary computational expense to determine them was avoided.

5 Case study overview

The case study was motivated by the need to introduce novel technologies in the design of a new heavy truck. A number of concepts were considered with a dual-use design philosophy in mind. Two powertrain systems were considered for propulsion to improve fuel efficiency: electric and series hybrid-electric, both using lead-acid batteries and in-hub motors for torque delivery at the wheels. Different variable height suspensions were


considered for the four axles of the truck to provide mobility and transportability. The baseline truck had a gross vehicle weight (GVW: curb weight plus payload) of 22 927 kg and a gross combined vehicle weight (GCVW: GVW plus trailer) of 38 886 kg. The baseline specifications of the V6, turbocharged, intercooled diesel engine were: 12.7 l displacement, 15:1 compression ratio, and 350 kW rated power at 2100 rpm.

After the development of the necessary simulation models, as described in the previous sections, the ATC case study was implemented based on a bi-level hierarchy with the top-level problem representing the truck and the four system-level problems representing the four individual suspensions. It is emphasised that during this first stage of the case study, the engine was not considered as a system at the system level; it was merely represented at the vehicle level as an engine map within the vehicle model. The ANN was not used, and the engine map was simply scaled linearly during the optimisation process.

Vehicle-level local design variables included engine scaling, number of battery modules, state of charge (SOC) limits, battery charging point, generator gear ratio, motor scaling (same for all in-hub motors), final drive, and power distribution ratios for the four axles. Vehicle-level response design variables included stiffness and damping for the four suspensions. Geometry characteristics of the four suspensions constituted the system-level local design variables.

Six truck design targets were identified: fuel economy at GVW and GCVW, absorbed power at GVW, maximum speed on flat road at GVW, maximum speed on a 2 per cent grade at GCVW, and maximum speed degradation from GVW to GCVW on flat road. Two sets of target values were defined: the first set imposed a fuel economy target value corresponding to a 50 per cent improvement relative to an existing heavy truck (i.e. 3.9 mpg at GVW and 2.3 mpg at GCVW), an absorbed power target value corresponding to a 1200 per cent improvement of required standards (i.e. 0.5. W at GVW), and performance target values corresponding to maintaining current characteristics (i.e. 55 mph maximum speed at GVW on flat road, 50 mph maximum speed at GCVW on 2 per cent grade, and 20 per cent maximum speed degradation from GVW to GCVW on flat road). The second set of target values asked for maximal improvement of the six design attributes (i.e. zero or infinity for minimisation or maximisation targets, respectively).

A driving scenario was defined for the assessment of fuel efficiency, ride quality, and performance. The truck was assumed to access a network of roads consisting of four sections corresponding to rough trails, trails, secondary road, and primary roads. Appropriate velocities were defined in the driving cycle for each of these sections, while road profiles were defined in terms of root mean square (RMS) elevation. The duration of a simulation was 910 real-time seconds. A state of charge correction was necessary to ensure proper fuel efficiency comparisons. The initial SOC is set equal to the maximum limit, which is a design variable. For most trial designs, the SOC at the end of the simulation would not correspond to the initial one. In this case, the engine-driven generator continued recharging the batteries until the initial SOC was reached. The additional fuel consumption was then taken into account.

The sequential quadratic programming (SQP) algorithm was used to solve the optimisation problems as formulated in Sections 2.1 and 2.2. The following observations were made:

• The fuel economy target values of the first set were achieved both for GVW and GCVW.


• The series hybrid-electric propulsion system yielded better fuel efficiency.

• The absorbed power target value of the first set was achieved.

• All GVW-related performance target values of the first set were achieved.

• GCVW-related performance attributes were improved, but the first set target values were not achieved.

• The results obtained using the second set of target values were insignificantly different.

• The engine and motor scaling variables and the final drive variable reached their respective upper bounds.

• Suspensions specifications and designs were nearly identical.

• Power was distributed uniformly to the four axles.

Details of this first stage of the case study can be found in Michelena et al. (2001). The following modifications and extensions were made based on the above

observations: GVW-related targets were omitted since they were all satisfied. A single set of target values was defined for improving fuel economy and absorbed power at GCVW and maintaining maximum speed degradation from GVW to GCVW. The GCVW fuel economy target value was increased to 3 mpg, while target values were kept the same for absorbed power (0.5 W) and maximum speed degradation on flat road (20 per cent). Only the constraint related to the maximum speed at GCVW on 2 per cent grade was included since it dominates the performance constraint for the maximum speed at GVW on flat road. However, the ‘target’ value for this constraint was reduced from 50 mph to 40 mph, since it was observed that the former cannot be achieved. Only the series hybrid-electric propulsion system was considered since it yielded better fuel efficiency. Additional battery types (lithium-ion and nickel metal hydride) were considered to investigate the effects of electrical components. Engine scaling was replaced by treating the engine map (computed using the radial basis function artificial neural network described in Section 3.1) at the vehicle level as a design variable. The engine was included at the system level so that vehicle design targets could also be translated to engine specifications. Two individual suspension systems were considered instead of four: one for the two front axles and one for the two rear axles. The location and suspension characteristics of the driver’s seat were included as design variables at the vehicle level. Finally, a more aggressive driving schedule was defined to assess ride quality, performance, and regenerative braking benefits. This resulted in a longer simulation (2150 real-time sec). Figures 16 and 17 depict desired velocity versus time and road elevation and slope versus distance, respectively. Such a schedule is typically used for heavy trucks. The rough road profile, indicated by high absolute slope values, during the first part of the schedule is necessary for an accurate evaluation of ride quality in terms of absorbed power measured at the driver’s seat. This driving scenario also aims at assessing the effect of regenerative braking on fuel economy. The batteries are charged during the decelerations and the downhill sections in the first and second parts of the schedule, respectively.


Figure 16 Driving cycle.

Figure 17 Road profile.

The findings of this extended study are summarised as follows.

• The new fuel economy target at GCVW was not achieved using any of the three considered battery types.

• The absorbed power target was always achieved.

• The maximum speed degradation target was achieved only when using NiMH batteries.

• The battery size was lower when using Pb relative to using Li or NiMH.

• As expected, optimal values of maximum and minimum SOC limits and charging point were different when using different battery types.


• Motor scaling and final drive variables attained their maximum allowable values

with the sole exception of the motor size in the Pb battery configuration.

• It was observed that the optimal values of the variables related to the suspension problems were not unique.

• The driver’s seat location did not vary significantly, and different seat suspension characteristics did not affect the absorbed power.

6 Enhanced optimisation technique

A composite optimisation technique is used to address issues related to the presence of local optima. Although a multistart strategy was employed previously to avoid local optima when solving the optimisation problems at the vehicle and system levels, it is imperative that derivative-free optimisation algorithms are used to draw final conclusions in simulation-based design. We reduce the number of variables to facilitate the use of global optimisation techniques. In addition, we consider introducing additional design constraints in an effort to reduce degrees of freedom of the variables related to the suspensions in the vehicle-level problem. These constraints restrict the pitch and heave frequency range of the suspension responses.

Figure 18 Coordination and information flow of the ATC process.

We use the same design target values: the fuel economy target values at GCVW is 3 mpg; absorbed power has to be at most 0.5 W on average; maximum speed degradation from GVW to GCVW on flat road cannot exceed 20 per cent. A single performance constraint dictates that the maximum speed at GCVW on a 2 per cent grade has to be at


least 40 mph. Finally, a simulation-related constraint is included to ensure that the truck velocity does not deviate from the desired velocity of the driving cycle by more than one mph on average.

The coordination and information flow of the ATC process is illustrated in Figure 18. Targets and responses are shown in octagons, design variables in trapezoids, optimisers in rectangles, and analysis/simulation models in ovals.

The vehicle-level problem is solved first to determine optimal vehicle design variables (number of battery modules, SOC limits, battery charging point, generator gearbox ratio, motor size, final drive) and system response design variable (torque map and fuelling curve for the engine and damping and compliance for the front and rear suspensions). We use the following composite optimisation technique to solve the vehicle design problem: we first solve the optimal design problem using the derivative-free algorithm DIRECT (Jones et al., 1993; Jones, 2001).

This algorithm features a balanced global and local search as opposed to other derivative-free algorithms. Thus, we are able to obtain satisfactory designs with a relatively low number of function evaluations. DIRECT stops when the prespecified number of function evaluations is reached, set to 4000 (approximately 250 × n, where n = 15 is the number of design variables). If necessary, i.e. if the design found by DIRECT does not meet all design targets, the Matlab Optimisation Toolbox implementation of the SQP algorithm is used with the DIRECT results as initial guess to improve the design.

Once optimal system response design variables are determined by solving the vehicle-level problem, their values are cascaded to the bottom level, where the three system design problems are solved independently to match them. System design variables for the engine and the two suspension problems consist of engine characteristics and suspension geometry variables, respectively. We use DIRECT to avoid local minima when solving the suspension design problems. However, we use SQP to solve the engine problem since a good initial guess is available from solving the vehicle-level problem by means of the neural network approach. After solving the system-level problems, the updated system response values are passed up to the top level, and the vehicle design problem is solved again using SQP since the design obtained previously serves as a good initial guess. The ATC process is declared as converged when the ∈ terms are below a use-specified tolerance, typically 1 per cent. In our case, this happens after two iterations. Such rapid convergence is expected for a bi-level hierarchy when the system-level subproblems are not coupled (systems do not share any design variables). In general, if response matching is unsatisfactory the whole process is repeated in an iterative manner until convergence is achieved.

7 Results and discussion

The vehicle attribute values obtained for the three battery types are compared in Figure 19. Results are normalised with respect to target values. Note that once a response achieves or exceeds its target value, it becomes ‘neutral’ to the optimiser, i.e. it does not contribute to the objective function.

Using the composite optimisation technique enabled us to find optimal designs that improved fuel economy relative to the results obtained previously. We are now able to


conclude that the Pb battery type (proposed initially in the first concept) yields the best fuel efficiency for the modelled truck configuration. However, the target was also met using Li batteries, and nearly achieved when using NiMH batteries. The results related to the ride quality attribute confirm again that the absorbed power target can always be met.

Figure 19 Normalised vehicle attribute values for the three battery types.

Finally, the maximum speed degration target can be met using any of the three battery types. Moreover, the performance characteristics of the heavy truck have been improved relative to the ones obtained previously.

Table 3 Relevant design target values and initial, improved, and final optimal attribute values ([C] and [N/A] denote constraint ‘target’ value, and ‘not applicable’, respectively).

Attribute Target value Initial Improved Final PB Li NiMH Pb Li NiMH Pb

Fuel economy at GCVW [mpg]

≥3 2.44 2.84 2.70 2.70 3.00 2.90 3.13

Absorbed power at GCVW [W]

≤0.5 0.27 0.14 0.49 0.40 0.45 0.41 0.38

Max. speed degr. On flat road [%]

≤20 20.6 21.35 0.01 21.83 19.93 19.94 19.83

Max. speed at GCVW on 2% grade road [mph]

≥40 [C] 40.76 41 45 41 45.60 45.82 45.94

Max. speed at GVW on flat road [mph]

[N/A] 85.45 86 90 86 90.93 90.96 91.29


Table 3 includes relevant design target values and summarises initial, improved, and final optimal attribute values as obtained throughout the case study. Tables 4 to 7 present optimal vehicle design and response (i.e. system specifications) variable values and optimal system design variable values.

Table 4 Optimal vehicle local design and response variable values computed at the vehicle level.

Local design variable Li NiMH Pb

Battery energy [Ah] 3626 1516 1422 Min SOC[-] 0.54 0.36 0.39 Max SOC [-] 0.65 0.64 0.80 Charging point SOC [-] 0.74 0.60 0.59 Motor gear ration [-] 28.18 27.46 28.62 Motor torque scale [-] 1.40 1.10 1.36 Generator gear ration [-] 1.88 2.32 2.26

Response variable

Front susp. Stiffness [N/m] 2.08 × 103 2.20 × 105 2.02 × 103

Front susp. Damping [Ns/m] 12326 14515 11541 Rear susp. Stiffness [N/m] 1.58 × 106 1.19 × 106 1.15 × 106

Rear susp. Damping [Ns/m] 16676 14795 18765

Table 5 Optimal engine local design variable values computed at the system level.


Displacement [l] 12.72 12.84 13.86 Compression ratio [-] 20.71 20.22 19.65 Max boost pressure [atm]

2.58 2.48 2.48

Wastegate activation point [rpm]

1945 1849 1974

Since the engine system specifications, i.e. the torque map and fuelling curve, cannot

be represented by single numbers, we present three plots that illustrate the matching between vehicle- and system-level contours and curves in Figure 20. The agreement is considered satisfactory for the purpose of the ATC process. An important point to note is that the entire engine map was calculated using one injection timing, to avoid the computational expense associated with a high-fidelity, ‘internal’ injection timing optimisation scheme as described in Section 3.1. That is, when the vehicle-level response was matched at the system-level, a compromised injection timing schedule was used. It was assumed that the deviation between optimal values of the high- versus low-fidelity methods would be acceptably small since at least 90 per cent of the computational need was prevented. This conclusion was drawn from past experience with similar systems. Also note that during the procedure of matching the engine map and fuelling curve to the vehicle-level responses, the fuelling curve pairs were constrained to be within 5 per cent


of each other at each calculated point on the fuelling curve. The objective was to minimise the difference between the torques on corresponding grid locations of fuel and speed under the fuelling curves. In general, the resulting matched data exhibited constraint activity along the fuelling curves, while the deviations of the overlapping torque values are negligible.

These results allow us to make the following final observations and conclusions: • All targets are achieved except the fuel economy target when using NiMH

batteries, which is missed by only 3 per cent. • When using Li batteries, a higher battery energy is necessary relative to using

NiMH or Pb batteries. • The difference between the minimum and maximum SOC limits decreases with

increasing battery energy • The charging point increases with increasing battery energy. • The generator gear ratio is higher for lower energy capacity. • A high motor final drive is necessary to satisfy the performance constraints. • The motor cannot be downsized for the same reason. • The stiffness suspension characteristics are similar when using all three battery

types. • Rear suspensions need to be stiffer than the front ones. • The damping suspension characteristics are not similar for all three battery

types. • Higher damping seems to be desirable for the rear suspensions when using Li

and Pb batteries. • The engine designs are very similar for all three battery types. • Relative to the lower and upper bounds, engine size (represented by

displacement), max boost pressure, and wastegate activation point are moderate, while compression ratio is high.

Table 6 Optimal front suspension local design variable values computed at the system level.


High pressure piston radius RS [m]

0.0317 0.0287 0.0193

Low pressure piston radius RP [m]

0.1272 0.1231 0.0800

Orifice radius R12 [m] 0.0126 0.0115 0.0093 Wheel hub location LH [m]

0.5859 0.5898 0.5652

Road hitch point coordinates (X3, Y3)

(0.0232,0.0807) (0.0173,0.0772) (0.0118,0.0757)

Rod length LR [m] 0.4786 0.4867 0.4344

Trailing angle α [rad] 0.4656 0.4512 0.6963


Table 7 Optimal rear suspension local design variable values computed at the system level.


High pressure piston radius RS [m]

0.0172 0.0173 0.0359

Low pressure piston radius RP [m]

0.0753 0.0752 0.1252

Orifice radius R12 [m] 0.0102 0.0102 0.0132 Wheel hub location LH [m]

0.5733 0.5757 0.5736

Road hitch point coordinates (X3, Y3)

(0.0981,0.0747) (0.0990,0.0750) (0.0237,0.0841)

Rod length LR [m] 0.4890 0.4830 0.4470

Trailing angle α [rad] 0.4417 0.4403 0.4856

Figure 20 Engine matching (torque map and fuelling curve) results for the three battery types; stars: vehicle-level; dots: system-level.


8 Conclusions

The analytical target cascading process has been applied to the optimal design of an advanced heavy truck. A bi-level model hierarchy was defined with the truck modelled at the top level and the engine and suspensions modelled at the bottom level. Novel technologies, such as a series hybrid-electric propulsion system, in-hub motors, and variable height suspensions were introduced with the intention of improving both commercial and military design attributes according to a dual-use philosophy. Emphasis was given to fuel economy, ride, and mobility characteristics. Three types of battery were considered to study their effect on fuel economy, and an aggressive driving schedule was used to assess regenerative braking benefits and ride quality. A composite optimisation technique was used to avoid convergence to local optima. Design targets were translated to system specifications for the engine and the front and rear suspensions that ensure consistent optimal truck design. The fuel efficiency target was exceeded, achieved, and missed by 3 per cent when using Lead-Acid, Lithium-Ion, and Nickel-Metal Hydride batteries, respectively. The ride quality and performance targets were exceeded and met for any of the considered battery types, respectively.

It is important to keep in mind that the findings of this case study depend on the defined driving cycle, operating and environmental conditions, hybrid power management and control strategies, and target values. Therefore, it is necessary to consider a variety of the aforementioned parameters to draw final conclusions. However, this extensive case study has demonstrated that the analytical target cascading process is quite useful in determining system design specifications that result into overall system optimality and consistency.

Acknowledgements

This research was partially supported by the Automotive Research Center, a US Army Center of Excellence in Modeling and Simulation of Ground Vehicles. This support is gratefully acknowledged. The authors would also like to thank Chan-Chiao Lin and Huei Peng for the design of the power management controller, and Mark Feury of USA-TACOM/TARDEC for his feedback and guidance.

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