A method for the optimal design of complex systems is developed by effectively combining multi-objective optimization and analytical target cascading techniques. The complex systems with high dimensionality are partitioned into manageable subsystems that can be optimized using dedicated algorithms. The multiple objective functions in each subsystem are treated simultaneously, and the interactions between subsystems are managed using linking variables and shared variables. The analytical target cascading algorithm ensures the convergence of the optimal solution that meets the system level targets while complying with the subsystem level constraints. A design optimization of electric vehicles with in-wheel motors is formulated as a two-level hierarchical scheme where the top level has a model representing the electric vehicle and the bottom level contains models of battery and suspension. The vehicle model includes an electric motor model and a power electronics model. Pareto-optimal solutions are derived holistically. The effectiveness of the proposed method for optimizing the complex systems is compared against the conventional all-in-one optimization approach.

References

1.
Kim
,
H. M.
,
Michelena
,
N. F.
,
Papalambros
,
P. Y.
, and
Jiang
,
T.
,
2003
, “
Target Cascading in Optimal System Design
,”
ASME J. Mech. Des.
,
125
(
3
), pp.
474
480
.
2.
Michelena
,
N.
,
Park
,
H.
, and
Papalambros
,
P. Y.
,
2003
, “
Convergence Properties of Analytical Target Cascading
,”
AIAA J.
,
41
(
5
), pp.
897
905
.
3.
Kianifar
,
M. R.
, and
Campean
,
I. F.
,
2014
, “
Analytical Target Cascading Framework for Engine Calibration Optimisation
,”
Int. J. Powertrains
,
3
(
3
), pp.
279
302
.
4.
Li
,
Z.
,
Kokkolaras
,
M.
,
Papalambros
,
P.
, and
Hu
,
S. J.
,
2008
, “
Product and Process Tolerance Allocation in Multistation Compliant Assembly Using Analytical Target Cascading
,”
ASME J. Mech. Des.
,
130
(
9
), p.
091701
.
5.
Michalek
,
J. J.
,
Feinberg
,
F. M.
, and
Papalambros
,
P. Y.
,
2005
, “
Linking Marketing and Engineering Product Design Decisions Via Analytical Target Cascading
,”
J. Prod. Innov. Manage.
,
22
(
1
), pp.
42
62
.
6.
Marler
,
R. T.
, and
Arora
,
J. S.
,
2010
, “
The Weighted Sum Method for Multi-Objective Optimization: New Insights
,”
Struct. Multidiscipl. Optim.
,
41
(
6
), pp.
853
862
.
7.
D’Errico
,
G.
,
Cerri
,
T.
, and
Pertusi
,
G.
,
2011
, “
Multi-Objective Optimization of Internal Combustion Engine by Means of 1D Fluid-Dynamic Models
,”
Appl. Energy
,
88
(
3
), pp.
767
777
.
8.
Mastinu
,
G.
,
Gobbi
,
M.
, and
Miano
,
C.
,
2007
,
Optimal Design of Complex Mechanical Systems: With Applications to Vehicle Engineering
,
Springer Science & Business Media
,
New York
.
9.
Deb
,
K.
,
2001
,
Multi-Objective Evolutionary Algorithms
, vol. 16,
John Wiley & Sons
,
Hoboken, NJ
.
10.
Ramakrishnan
,
K.
,
Gobbi
,
M.
, and
Mastinu
,
G.
,
2015
, “
Multi-Objective Optimization of In-Wheel Motor Powertrain and Validation Using Vehicle Simulator
,”
2015 Tenth International Conference on EVER
,
Monte Carlo
,
Mar. 31–April 2
, IEEE, pp.
1
9
.
11.
Ramakrishnan
,
K.
,
Yang
,
L.
,
Ballo
,
F. M.
,
Gobbi
,
M.
, and
Mastinu
,
G.
,
2016
, “
Multi-Objective Optimization of Road Vehicle Passive Suspensions With Inerter
,”
ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
,
Charlotte, NC
,
Aug. 21–24
, American Society of Mechanical Engineers, pp.
V003T01A007
V003T01A007
.
12.
Zhang
,
B.
,
Chen
,
Z.
,
Mi
,
C.
, and
Murphey
,
Y. L.
,
2009
, “
Multi-Objective Parameter Optimization of a Series Hybrid Electric Vehicle Using Evolutionary Algorithms
,”
2009 IEEE Vehicle Power and Propulsion Conference (VPPC’09)
,
Dearborn, MI
,
Sept. 7–10
, IEEE, pp.
921
925
.
13.
Ramakrishnan
,
K.
,
Curti
,
M.
,
Zarko
,
D.
,
Mastinu
,
G.
,
Paulides
,
J. J.
, and
Lomonova
,
E. A.
,
2017
, “
Comparative Analysis of Various Methods for Modelling Surface Permanent Magnet Machines
,”
IET Electr. Power Appl.
,
11
(
4
), pp.
540
547
.
14.
Zhu
,
Z.
,
Howe
,
D.
,
Bolte
,
E.
, and
Ackermann
,
B.
,
1993
, “
Instantaneous Magnetic Field Distribution in Brushless Permanent Magnet DC Motors. I. Open-Circuit Field
,”
IEEE Trans. Magn.
,
29
(
1
), pp.
124
135
.
15.
Žarko
,
D.
,
Ban
,
D.
, and
Lipo
,
T.
,
2008
, “
Analytical Solution for Cogging Torque in Surface Permanent-Magnet Motors Using Conformal Mapping
,”
IEEE Trans. Magn.
,
44
(
1
), pp.
52
65
.
16.
Boughrara
,
K.
,
Zarko
,
D.
,
Ibtiouen
,
R.
,
Touhami
,
O.
, and
Rezzoug
,
A.
,
2009
, “
Magnetic Field Analysis of Inset and Surface-Mounted Permanent-Magnet Synchronous Motors Using Schwarz–Christoffel Transformation
,”
IEEE Trans. Magn.
,
45
(
8
), pp.
3166
3178
.
17.
Gysen
,
B. L. J.
,
Meessen
,
K. J.
,
Paulides
,
J. J. H.
, and
Lomonova
,
E. A.
,
2010
, “
General Formulation of the Electromagnetic Field Distribution in Machines and Devices Using Fourier Analysis
,”
IEEE Trans. Magn.
,
46
(
1
), pp.
39
52
.
18.
Sprangers
,
R.
,
Paulides
,
J.
,
Gysen
,
B.
, and
Lomonova
,
E.
,
2016
, “
Magnetic Saturation in Semi-analytical Harmonic Modeling for Electric Machine Analysis
,”
IEEE Trans. Magn.
,
52
(
2
), pp.
1
10
.
19.
Zarko
,
D.
,
Ban
,
D.
, and
Lipo
,
T.
,
2006
, “
Analytical Calculation of Magnetic Field Distribution in the Slotted Air Gap of a Surface Permanent-Magnet Motor Using Complex Relative Air-Gap Permeance
,”
IEEE Trans. Magn.
,
42
(
7
), pp.
1828
1837
.
20.
Gobbi
,
M.
,
Levi
,
F.
, and
Mastinu
,
G.
,
2006
, “
Multi-Objective Stochastic Optimisation of the Suspension System of Road Vehicles
,”
J. Sound Vib.
,
298
(
4
), pp.
1055
1072
.
21.
Guarneri
,
P.
,
Gobbi
,
M.
, and
Papalambros
,
P. Y.
,
2011
, “
Efficient Multi-Level Design Optimization Using Analytical Target Cascading and Sequential Quadratic Programming
,”
Struct. Multidiscipl. Optim.
,
44
(
3
), pp.
351
362
.
22.
Tosserams
,
S.
,
Etman
,
L.
,
Papalambros
,
P.
, and
Rooda
,
J.
,
2006
, “
An Augmented Lagrangian Relaxation for Analytical Target Cascading Using the Alternating Direction Method of Multipliers
,”
Struct. Multidiscipl. Optim.
,
31
(
3
), pp.
176
189
.
23.
Mastinu
,
G.
, and
Ploechl
,
M.
,
2014
,
Road and Off-Road Vehicle System Dynamics Handbook
,
CRC Press
,
Boca Raton, FL
.
24.
Ramakrishnan
,
K.
,
Romanazzi
,
P.
,
Zarko
,
D.
,
Mastinu
,
G.
,
Howey
,
D. A.
, and
Miotto
,
A.
,
2017
, “
Improved Analytical Model of an Outer Rotor Surface Permanent Magnet Machine for Efficiency Calculation With Thermal Effect
,”
SAE Int. J. Altern. Powertrains
,
6
(
1
), pp.
34
46
.
25.
Stipetic
,
S.
,
Zarko
,
D.
, and
Popescu
,
M.
,
2016
, “
Ultra-Fast Axial and Radial Scaling of Synchronous Permanent Magnet Machines
,”
IET Electr. Power Appl.
,
10
(
7
), pp.
658
666
.
26.
Žarko
,
D.
,
2004
, “
A Systematic Approach to Optimized Design of Permanent Magnet Motors With Reduced Torque Pulsations
,” PhD thesis,
Department of Electrical and Computer Engineering, University of Wisconsin-Madison
,
Madison, WI
.
27.
Gieras
,
J.
,
2011
,
Permanent Magnet Motor Technology: Design and Applications
, 3rd ed,
Electrical and Computer Engineering, CRC Press
,
London
.
28.
De Doncker
,
R.
,
Pulle
,
D. W.
, and
Veltman
,
A.
,
2010
,
Advanced Electrical Drives: Analysis, Modeling, Control
,
Springer Science & Business Media
,
New York
.
29.
Iqbal
,
A.
,
Ahmed
,
S. M.
,
Khan
,
M. A.
, and
Abu-Rub
,
H.
,
2010
, “
Generalised Simulation and Experimental Implementation of Space Vector PWM Technique of a Three-Phase Voltage Source Inverter
,”
Int. J. Eng. Sci. Technol.
,
2
(
1
), pp.
1
12
.
30.
Wu
,
B.
, and
Narimani
,
M.
,
2017
,
High-Power Converters and AC Drives
,
John Wiley & Sons
,
New York
.
31.
Hassan
,
W.
, and
Wang
,
B.
,
2012
, “
Efficiency Optimization of PMSM Based Drive System,” 2012 7th International Power Electronics and Motion Control Conference (IPEMC)
, Vol.
2
, Harbin, China, IEEE, pp.
1027
1033
.
32.
U.S. Government Printing Office
,
1981
, “
The Code of Federal Regulations of the United States of America
,” Washington, CRF 420.1, p.
10
.
33.
Romanazzi
,
P.
,
Galizzi
,
V.
,
Carbone
,
F.
,
Miotto
,
A.
, and
Howey
,
D.
,
2016
, “
Improved Thermal Equivalent Circuit Element Applied to an External Rotor SPM Machine
,”
2016 XXII International Conference on ICEM
, Lausanne, Switzerland, IEEE, pp.
2718
2724
.
34.
Gobbi
,
M.
, and
Mastinu
,
G.
,
2001
, “
Analytical Description and Optimization of the Dynamic Behaviour of Passively Suspended Road Vehicles
,”
J. Sound Vib.
,
245
(
3
), pp.
457
481
.
35.
Scheibe
,
F.
, and
Smith
,
M. C.
,
2009
, “
Analytical Solutions for Optimal Ride Comfort and Tyre Grip for Passive Vehicle Suspensions
,”
Veh. Syst. Dyn.
,
47
(
10
), pp.
1229
1252
.
36.
D’Errico
,
J.
,
2005
, “
Bound Constrained Optimization Using Fminsearch: Fminsearchbnd
,” matlab® Central.
37.
Miettinen
,
K.
,
2012
,
Nonlinear Multiobjective Optimization
, Vol.
12
,
Springer Science & Business Media
,
New York
.
You do not currently have access to this content.