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Abstract—Simulation-based design optimization of an electric
vehicle (EV) propulsion system requires integration of a system
model with detailed models of the components. In particular, a
high fidelity interior permanent-magnet (IPM) motor model is
necessary in order to capture important physical effects, such as
magnetic saturation. The system optimization challenge is to
maintain adequate model fidelity with acceptable computational
cost. This paper proposes a design method that incorporates
high-fidelity motor, high-voltage power electronics, and vehicle
propulsion simulation models in a system design optimization
formulation that maximizes energy efficiency of a compact EV on
a given drive cycle. The resulting optimal design and associated
energy efficiency for a variety of drive cycles and performance
requirements are presented and discussed.
Index Terms— Electric vehicle, Vehicle electrification, Motor
design, Design optimization, Optimal design
I. INTRODUCTION
HE propulsion system design process requires
integrating sub-system (component) designs into an overall
system model in order to maximize the performance of a given
propulsion architecture [1]. Previous studies have shown that
vehicle fuel efficiency and performance depend substantially
on how the design problems are coordinated [2]. Good
integration requires coordination of sub-system models and
requisite model interfaces that enable the virtual integration of
all system elements.
In Battery Electric Vehicle (BEV) design, ideal integration
will capture inter-dependency between motor and vehicle
system design. Changes resulting from a new motor design are
analyzed and taken into account on the system design side, and
vice versa. For example, new motor performance with a new
motor stack length requires a new optimal final drive ratio,
This paper was first submitted on March 11, 2014 for review.
Copyright (c) 2013 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be
obtained from the IEEE by sending a request to [email protected].
Kukhyun Ahn was with the Mechanical Engineering Department, University of Michigan, Ann Arbor, MI 48109 USA (e-mail:
A. E. Bayrak is with the Mechanical Engineering Department, University of Michigan, Ann Arbor, MI 48109 USA (e-mail: [email protected])
P.Y. Papalambros is with the Mechanical Engineering Department and
Division of Integrated Systems & Design, University of Michigan, Ann Arbor, MI 48109 USA (email: [email protected])
which shifts motor operation points. On the motor design side,
stack length must be optimized again given the shifted
operation points.
In earlier integration efforts in BEV design, motor rating
optimization used scaled maps derived from a baseline map in
order to find an approximate motor rating given vehicle
propulsion system and performance requirements [3,4]. This
method, however, is limited in capturing detailed
electromagnetic characteristics and geometric information of a
motor design, thus confining its application to the early
conceptual design stage.
Practical electric propulsion system design typically requires
a high-fidelity motor model based on Finite Element Analysis
(FEA) or other analysis methods of comparable accuracy.
Some methods employ detailed FEA for high fidelity in motor
modeling [5-15], and other methods use non-FEA motor
analyses to reduce computation time for running a large number
of simulations [14-23].
While these modeling and analysis methods provide high
analysis accuracy and efficiency, direct integration of a motor
model into a system optimization model has high
computational cost. Thus, the motor design remains at the
sub-system level, only allowing for motor design changes given
vehicle system design.
Some integration strategies that address design
inter-dependency are based on decomposition. In a common
formulation, vehicle performance at the system level is
translated to motor target performance at the motor design level
[1,24]. Another common formulation bases motor design on
subsystem use information obtained from system-level
simulation [2]. In order for these formulations to capture design
inter-dependency, they require an iterative solution process,
such as Augmented Lagrangian Coordination and Analytic
Target Cascading [1,24]. The challenge for these integration
strategies is to coordinate the motor design requirements with
the overall system design requirements, maintaining
consistency in the boundary conditions across the elements of
the decomposed system.
In contrast to decomposition-based integration, All-in-One
(AIO) integration requires little coordination effort because the
entire system is simultaneously analyzed and optimized.
However, interfacing individual design spaces is difficult and
rarely discussed in the literature. A method that builds a
metamodel of a high-fidelity motor model and integrates the
Electric Vehicle Design Optimization:
Integration of a High-fidelity Interior
Permanent-Magnet Motor Model
Kukhyun Ahn, Alparslan Emrah Bayrak, and Panos Y. Papalambros
T
This is the author's version of an article that has been published in this journal. Changes were made to this version by the publisher prior to publication.The final version of record is available at http://dx.doi.org/10.1109/TVT.2014.2363144
Copyright (c) 2014 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by emailing [email protected].
VT-2014-00407.R1
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metamodel directly into a system optimization model was
previously presented [2]. An alternative approach is proposed
in this paper referred to as an indirect integration strategy.
In this integration study, an IPM synchronous motor is
designed as part of a BEV propulsion system. The integrated
problem is solved in an AIO optimization formulation, where
an FEA-based high-fidelity motor model is incorporated into a
feed-forward vehicle simulation model. Key power electronics
devices are also modeled in order to include electric power
control decisions in the optimization problem. We discuss how
to integrate the motor and propulsion models and create a
unified design space where design variables of the motor,
power electronics, and vehicle propulsion models are
optimized simultaneously.
In Section 2, the sub-system and system models are
described. Section 3 details the method of creating a unified
design space for BEV propulsion. Optimization results are
presented in Section 4, followed by some discussion and
conclusions in Section 5.
II. BEV PROPULSION SYSTEM MODELING
In model-based system analysis and design of electric
vehicles, sufficiently high fidelity is required for key
sub-systems such as electric motors, power electronics, and
battery systems. Once an adequate level of model fidelity is
achieved, the challenge is to integrate the high-fidelity models
into a system-level vehicle model.
The modeling effort focuses on the IPM motor and the
vehicle, including the high-voltage electric drive, gear-train,
and resistive road loads. The schematic of the BEV propulsion
system is shown in Fig. 1. Dashed and solid lines represent
electrical and mechanical connections, respectively. The design
variables that represent the respective component models are
shown in parentheses.
A. IPM Synchronous Motor
The analysis of motor design here is based on SPEED
software [25]. Two-dimensional FEA is run using
parameterized templates of cross-sectional designs (magnet,
stator tooth, etc.) combined with phasor diagram analysis to
achieve reduced computational cost compared to that of
full-scale FEA. Fig. 2 shows the modeling and FEA simulation
of a motor design in SPEED.
Three-phase AC is fed to the machine by a DC-AC inverter,
whose modeling details are given in the following subsection.
The baseline design has eight poles for permanent magnet
blocks and 12 stator slots for concentrated winding. The outer
and inner diameters are 250 and 150 mm, respectively. The air
gap is 1 mm.
Two design variables were chosen for the motor: coil turns of
the three-phase concentrated winding, and lamination stack
length. After some preliminary exploration of the design space,
the first was set to vary between 102 and 110 turns, and the
second between 140 and 160 mm. Each variable was assigned
five equally-spaced levels to generate 25 full-factorial design
samples, which represent the motor subsystem in the vehicle
design space. This way, the high-fidelity motor model can be
integrated in the vehicle design process with reasonable
computational cost. Determining the sampling method and
sample size depends on the problem dimension and complexity.
Here, we found the full-factorial sampling with five levels for
two factors sufficient for the problem, as discussed in the
results section.
For each of the sample designs, magnetic circuit and
mechanical loss data ( , , , ) are collected in the
two-dimensional operation space of control current ( ) and
angle ( ). Fig. 3 shows a flux surface on the current-angle grid.
For the grid fineness shown in the figure, the analysis time for a
sample design is about half an hour.
Given a machine rotational speed ( ), the d, q-axis phasor
properties are calculated as,
, , (1)
, , (2)
, , (3)
where electric speed is calculated by for the 8-pole
machine and is the phase resistance.
Then, line-to-line voltage ( ), output torque ( ) and input
power ( ) are obtained as,
Fig. 1. Electric vehicle propulsion and design variables
Fig. 2. Finite element analysis of IPM motor
This is the author's version of an article that has been published in this journal. Changes were made to this version by the publisher prior to publication.The final version of record is available at http://dx.doi.org/10.1109/TVT.2014.2363144
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VT-2014-00407.R1
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,
(4)
, (5)
, (6)
where , accounts for iron (core)
loss, copper loss is calculated by
, and
inverter loss, , is calculated using the models described in
the next subsection. The fluxes and currents are RMS (root
mean square) values.
A set of control current and angle is found to minimize input
power for the target shaft torque ( ), maintaining line-to-line
voltage below the DC voltage ( ). The optimization problem
is formulated as,
with respect to
subject to . (7)
Repeatedly solving the optimization problem sweeping
machine speed and target torque, a pair of a full-load torque and
power loss maps are generated for a corresponding DC voltage.
The two-stage map generation procedure is summarized in
Table I.
Setting five levels of DC voltages from 630 to 670 V
produced a total of 125 motor map pairs, representing a
three-dimensional design space of motor coil turns, lamination
stack length and DC operation voltage.
This indirect integration method enables virtual exploration
of the three-dimensional design space as a continuum and
avoids excessive computational cost. We discuss how the 125
map pairs are used to assess vehicle attributes and then build a
virtual continuum space in the vehicle propulsion analysis
subsection and optimization section further below.
B. High-Voltage Power Electronics Devices
The schematic of the circuit used in the power electronics
devices is shown in Fig. 4. The first two IGBTs (Insulated-Gate
Bipolar Transistors), Q1 and Q2, along with the capacitor and
inductor represent the DC/DC converter, and the other six
IGBTs represent the inverter. In the vehicle model, the power
electronics devices are modeled as loss components with a
simple input and output power relationship.
The losses at the power electronics stage are grouped into
switching and conduction losses. Switching losses consist of
three elements, turn-on and turn-off losses in the IGBTs and
turn-off loss in the diodes, each of which is a function of
switching voltage, current and frequency. The conduction loss
in the DC/DC converter is a function of battery current and duty
cycle, while the conduction loss in the inverter is a function of
peak current, modulation index and phase angle. Since only one
diode and one transistor from switches Q1 and Q2 conduct
during motor and generator operations, DC/DC converter loss
is calculated for a diode and a transistor [17]. The total loss in
the DC/DC converter is the sum of three switching losses
( ), conduction loss of a diode ( ), and conduction
loss of an IGBT ( ).
. (8)
The input and output power relationship is given by:
, (9)
where battery power ( ) and power at the DC-link ( ) are
negative in boost mode and positive in buck mode.
Similarly to the DC/DC converter, the inverter loss is
calculated for each transistor and diode pair and then multiplied
by six to obtain the total loss [17]. The total inverter loss is
given as follows:
=13( / ) , (10)
Fig. 3. Permanent magnet flux linkage
Fig. 4. Power electronics topology
TABLE I
MOTOR MAP GENERATION PROCEDURE
•Sweep control variables: Irms, γ •To obtain phasor properties
Stage 1: Finite element analysis
•Sweep operation variables: ωm, Tsh
•To obtain minimized power loss
Stage 2: Control optimization
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VT-2014-00407.R1
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where are three switching loss components, and
and are conduction losses of an IGBT and a
diode in the inverter, respectively.
C. Vehicle Propulsion
A compact-sized vehicle model was built in the software
environment AMESim [26] (See Fig. 5). The 1-D multi-domain
vehicle model includes models of the driver, control unit,
battery, IPM motor, single-ratio transmission (final drive),
power electronics, and resistive loads of the vehicle body.
The dynamic propulsion model is solved in a feed-forward
manner with a driver control, and power losses are calculated
using static look-up maps or resistive models in mechanical and
electrical components. The traction motor solely propels the
vehicle with a single-ratio reduction gear that multiplies motor
traction torque. Gear losses are modeled using a damper with a
constant damping ratio. Road load components such as rolling
resistance and aerodynamic drag are included in the vehicle
model. The motor weight varies with the IPM motor design
variables and is added to the base vehicle weight. On the
electrical side, a DC-DC converter and DC-AC inverter are
placed between the high-voltage battery and the motor to
achieve power controls.
The converter, inverter, motor, and battery are integrated in
the propulsion system via static loss models; see Fig. 6 for a
motor loss map example. The first three were described in the
earlier subsections. The battery model is based on a fixed cell
design and the pack arrangement. Each cell is modeled using
open circuit voltage ( ), internal resistance ( ) and
filtering capacitance ( ). Given a current demand from a cell
( ), the output voltage of the cell ( ) is calculated by
solving the following dynamic equation:
, (11)
where and are functions of the state of charge ( )
and calculated using look-up maps. A fixed value of 50 F is
used in this study. Also is calculated as follows:
, (12)
where is the nominal battery cell capacity. The battery
information is shown in Table II along with some other vehicle
parameters.
The propulsion model predicts the vehicle’s 0-60MPH
acceleration time and charge depletions on test drive cycles for
a given set of propulsion design variables. Three drive test
cycles are used in this study: FTP75, NEDC and US06. Fig. 7
shows the battery state of charge simulated on US06, along
with the cycle’s speed profile.
III. OPTIMIZATION
The proposed design method enables integration of
high-fidelity motor and EV propulsion design, and achieves
system integration following a sequential procedure, whose
steps are summarized in the flow diagram in Fig. 8. Four design
variables are given in parentheses.
In the first step of the procedure, design samples are chosen
to represent the motor design space with two design variables.
When analysis results are produced for the samples, one design
variable is added to incorporate the high-voltage DC operation
decision. This decision assumes fixed voltage not considering
variable voltage control. After motor control optimization
post-processing, pairs of motor loss and capacity maps are
generated for all combinations of the three design variables. For
each motor efficiency/full-load map pair, representing one
motor design and its operation voltage, vehicle simulations are
run repeatedly for a set of final drive values to assess energy
efficiency and performance of the vehicle designs. In this study,
five levels were chosen for each design variable (stack length,
coil turns, DC voltage and final drive ratio), resulting in 625 EV
designs. Depending on the design goals, design variables,
sampling methods, and sample sizes can be selected to suit the
goals. For example, more advanced sampling techniques can be
Fig. 5. Vehicle simulation model in AMESim
Fig. 6. Motor power loss as function of speed and torque
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VT-2014-00407.R1
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applied to find if they result in better model accuracy than the
full-factorial method that we chose here. Motor magnet shape
dimensions can be variables of choice instead of or in addition
to the current selection if design flexibility permits.
Battery charge depletions over NEDC, US06, and FTP75 are
calculated using AMESim vehicle simulation, as described in
an earlier section. The 0-60MPH acceleration time is also
simulated as a dynamic performance index. Based on the
simulation results, we build metamodels to represent the
function relationships between the design variables and the
corresponding vehicle attributes [3,4].
In the present study, we incorporate the motor
electromagnetic FEA and vehicle propulsion simulation into a
single AIO design space. This resolves the issue that both
high-fidelity analysis models are computationally too
expensive to be used for a large number of trial designs during
optimization. Although a limited number of design samples are
used, the built AIO surrogate design space performs as a
continuum, within which any design can be assessed at very
low computational cost. The key to validating the indirect
integration method is to ensure that prediction accuracy is
sufficiently high, as discussed in the results section.
For the metalmodels, we chose the RBF (Radial Basis
Function) interpolation after comparison with the quadratic
polynomial regression and the feed-forward artificial neural
network. The basis functions are multiquadrics and scaled to
minimize the mean leave-one-out error [27]. As shown in the
following section, the chosen metamodel is appropriate for the
complexity of the design space under consideration. More
sophisticated modeling and optimization techniques such as
Efficient Global Optimization (EGO) may be required if more
variables or model uncertainty were to be included in the motor
and vehicle design models [28-31].
Optimization is formulated as a bi-objective problem: the
two objectives are to minimize the battery charge depletion
over a cycle and to maximize 0-60MPH acceleration
performance at the same time. This is similar to a previously
proposed formulation, where one attribute is the sole objective
and the other is a constraint [2,32]. By repeatedly solving the
problem for several different bounds on the latter constraint, the
trade-off between the two attributes is found. Alternatively,
using Multi-Objective Genetic Algorithm (MOGA), the
bi-objective formulation gives a continuous view of the
trade-off frontier and design selections, as will be shown in the
next section. NSGA-II (Non-dominated Sorting Genetic
Algorithm-II) is employed [33, 34], and the initial population of
the sample designs is evolved through 10 generations. The four
design variables are motor armature coil turns, , stack
length, , operation DC voltage, , and final drive ratio,
. The optimization problem is formulated as,
with respect to
subject to the upper and lower bounds on , , , and
(13)
where and are the charge depletion and 0-60mph
acceleration time, respectively. The three test cycles are FTP75,
US06, and NEDC.
IV. RESULTS
Fig. 9 shows the attribute space in the case of the NEDC
cycle. The dots represent the attribute pairs of the 625 sample
EV designs. The lower charge depletion on the y-axis indicates
TABLE II
VEHICLE SPECIFICATIONS
Initial battery voltage 350 V
Pack configuration 90 cells in series, 2 modules in parallel
Battery cell capacity 33.1 Ah
Base vehicle weight 1521 kg
Frontal area 2.27 m2
Drag coefficient 0.29
Tire radius 0.316 m
Fig. 7. Vehicle velocity and battery state of charge
Fig. 8. Motor and EV propulsion integrated design flow
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VT-2014-00407.R1
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higher vehicle energy efficiency, and the smaller acceleration
time to 60 MPH on the x-axis indicates better performance. The
relationships between the designs and attributes, when captured
in a metamodel, led to Pareto-optimal solutions (solid curve),
found by the MOGA method. The curve represents the
marginal attribute pairs that the EV can achieve within the
given design constraints.
On the design space side, the solutions that correspond to
Pareto-optimal solutions in Fig. 9 are plotted in Fig. 10.
Along the Pareto frontier, each variable shows a noticeable
trend although discontinuity is observed due to local optima.
For example, higher DC voltage and final drive ratio contribute
to better performance but cause lower energy efficiency. We
can also infer that allocating more space for the motor in the
axial direction is likely to lead to a better BEV design.
However, these trends may not be perceived as separate
phenomena because they come from simultaneous interaction
among the four variables. Based on the obtained Pareto
frontiers, MPGe (Miles Per Gallon equivalent) has been
calculated for five performance target levels in the three cycle
cases [35]. Fig. 11 summarizes the optimization results.
As described earlier, optimization was based on prediction of
the vehicle attributes (acceleration and MPGe’s on three
cycles), and the prediction models (metamodels) need to be
checked for their validity. From the 15 optimal solutions in Fig.
11, 12 are from the metamodel prediction. When we performed
simulation for these 12 optimal designs, virtual and real
attributes matched closely, as can be seen in Fig. 12. The
percentage errors did not exceed 0.42 and 0.053 in the cases of
acceleration and MPGe, respectively. This indicates the
proposed approach represents motor performance with
sufficiently high accuracy in the integrated design space.
V. CONCLUSIONS
We proposed a method that integrates a high-fidelity motor
and vehicle analysis model for optimizing the IPM motor and
vehicle propulsion design simultaneously. Without actually
running a costly FEA simulation for every trial design, the
motor design space was accurately captured and efficiently
incorporated in the propulsion design space, i.e., high fidelity
was maintained for both motor and vehicle models.
Metamodel-based design optimization allowed for the
multi-domain analyses to be integrated: IPM motor FEA,
power electronics steady-state simulation and EV propulsion
forward-facing dynamic simulation. Once the functional
relationship from the design space to the attribute space is
modeled, the cost of exploring the integrated design space is
significantly reduced. We performed an extensive search using
MOGA and obtained the Pareto-optimal solutions for two
vehicle attributes, energy efficiency on US and European test
cycles and 0-60MPH acceleration performance. Driveability,
NVH, and safety metrics can be additionally taken into design
consideration in the form of objectives or constraints in this
optimization framework. Tracing the changes in optimal design
variable values as the objective changes showed how individual
variables affect the optimal design.
This integration study suggests that the approach used here
may also work for problems of higher complexity. Future
Fig. 9. Charge depletion on NEDC against acceleration
Fig. 10. Normalized optimal design solutions
Fig. 11. Energy efficiency on three test cycles
This is the author's version of an article that has been published in this journal. Changes were made to this version by the publisher prior to publication.The final version of record is available at http://dx.doi.org/10.1109/TVT.2014.2363144
Copyright (c) 2014 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by emailing [email protected].
VT-2014-00407.R1
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research can address inclusion of additional motor design
variables, such as radial dimensions (rotor, air gap and stator),
magnet block arrangements and stator tooth dimensions, as
well as power electronics and battery design variables. The
methodology can also be applied to integrate more detailed
electromagnetic analysis models or vehicle packaging
optimization models. To address higher design space
dimensionality, the number of motor design samples must be
significantly increased. Rapid motor analysis methods, such as
Output Spacing Mapping, may serve well for this purpose.
More sophisticated metamodel types can also be examined to
replace the RBF interpolation method used here to capture the
increased complexity.
ACKNOWLEDGMENT
This work was partially supported by the Automotive
Research Center, a US Army Center of Excellence in Modeling
and Simulation of Ground Vehicle Systems headquartered at
the University of Michigan. The LMS International and
CD-adapco provided academic support for the use of the
AMESim and SPEED software, respectively. This support is
gratefully acknowledged. The findings of this work reflect only
the opinion of the authors.
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This is the author's version of an article that has been published in this journal. Changes were made to this version by the publisher prior to publication.The final version of record is available at http://dx.doi.org/10.1109/TVT.2014.2363144
Copyright (c) 2014 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by emailing [email protected].
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Kukhyun Ahn received his B.S. (2000),
M.S. (2002) and Ph.D. (2007) degree in
mechanical engineering at Seoul National
University, Seoul, South Korea.
He was research faculty in Mechanical
Engineering at the University of Michigan,
Ann Arbor, USA and a visiting researcher
at General Motors Global R&D, Warren,
USA before joining Research and
Advanced Engineering at Ford Motor Company, Dearborn,
USA. His research interests include a wide range of topics in
vehicle electrification, such as hybrid electric propulsion
architectures, propulsion system energy management and
design optimization.
Alparslan Emrah Bayrak was born in
Aksehir, Konya, Turkey in 1988. He
received the B.S. degree in mechatronics
engineering from Sabanci University,
Istanbul, Turkey in 2011 and M.S. degree
in mechanical engineering from the
University of Michigan, Ann Arbor, MI, in
2013.
Since 2011, he has been a Research Assistant with the
Optimal Design Laboratory at the University of Michigan.
Since 2013 he has been a PhD candidate in mechanical
engineering at the University of Michigan. His research
interests include optimal design and control of electric and
hybrid electric powertrain architecture, modular vehicle design
and crowdsourced design with gaming platforms.
Panos Y. Papalambros is the James B.
Angell Distinguished University
Professor and the Donald C. Graham
Professor of Engineering. He is a
Professor of Mechanical Engineering,
Professor of Architecture, and Professor
of Art and Design; and serves as the
founding Chair of the Integrative
Systems & Design Division, College of
Engineering, at the University of Michigan.
Born in Patras, Greece, he attended the National Technical
University of Athens and earned a diploma in Mechanical and
Electrical Engineering in 1974. Moving to California he
attended Stanford University and earned his M.S. degree
(Mechanical Engineering) in 1976 and Ph.D. degree (Design
Division, Mechanical Engineering) in 1979. At Michigan he
has served as a faculty member since 1979. During his tenure at
Michigan he served as mechanical engineering department
chair (1992-98, and 2007-08) and was the founding director of
Optimal Design (ODE) Laboratory (1980-); Design Laboratory
(1990-92); Ford Durability Simulation Center (1992-94);
Automotive Research Center (1994-2003); General Motors
Collaborative Research Laboratory (1998-2002); the Antilium
Project (2003-2008), and the Ford BlockM Sustainability
Laboratory (2006-2009); he served as the founding chair and
director of the University of Michigan interdisciplinary Design
Science Doctoral Program (2006-2011). His research interests
include design science and optimization, with applications to
sustainable design of products, automotive systems, such as
hybrid and electric vehicles; design of complex engineered
systems; and architectural design. With D. J. Wilde, he
co-authored the textbook Principles of Optimal Design (1988,
2000). He has published over 320 articles in journals,
conference proceedings, and books.
He is a member of ASME, INFORMS, MOS, SME, SAE,
ISSMO, AIAA, AAUP, ASEE, IEEE, INCOSE and serves as
Vice President on the Board of Management of the Design
Society. He served as Chief Editor of the ASME Journal of
Mechanical Design (2008-2012) and as associate editor of the
Journal of Mechanisms, Transmissions and Automation in
Design, Journal of Global Optimization, Computer-Integrated
Engineering, and the Japan Society of Mechanical Engineers
International Journal. He currently serves on the editorial
boards of the journals Artificial Intelligence in Engineering
Design and Manufacturing, Engineering Design, Engineering
Optimization, Structural and Multidisciplinary Optimization,
Journal of Reliability and Safety and Product Development.
He is a Fellow of ASME and SAE, and the recipient of the
ASME Design Automation Award (1998), ASME Machine
Design Award (1999), Japan SME Design and Systems
Achievement Award (2004), ASME Joel and Ruth Spira
Outstanding Design Educator Award (2007), and the Stephen
S. Attwood Award (highest engineering honor in the University
of Michigan, 2009).
This is the author's version of an article that has been published in this journal. Changes were made to this version by the publisher prior to publication.The final version of record is available at http://dx.doi.org/10.1109/TVT.2014.2363144
Copyright (c) 2014 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by emailing [email protected].
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