This article deals with the dynamic response optimization of mechanical systems, based on the computation of independent state sensitivities. Specifically, the dynamic behavior of a coach is analyzed in detail so as to improve its response in terms of handling and ride comfort behaviors. To that end, the coach is modeled as an 18DOF multibody system, whose equations of motion are posed using an efficient dynamic formulation based on Maggi's equations. Next, a direct-automatic differentiation approach for the computation of independent state sensitivities is applied. This allows one to quantify the effect of 19 design parameters on the vehicle dynamic response and to compute the design sensitivities or objective function gradients. Finally, handling and ride comfort objective functions are defined and are used to carry out a multi-objective suspension design optimization process, improving the vehicle response by 70% in an effective yet automatic way.

References

References
1.
Bestle
,
D.
, and
Eberhard
,
P.
,
1992
, “
Analyzing and Optimizing Multibody Systems
,”
Mech. Struct. Mach.
,
20
(
1
), pp.
67
92
.10.1080/08905459208905161
2.
Pagalday
,
J.
, and
Avello
,
A.
,
1997
, “
Optimization of Multibody Dynamics Using Object Oriented Programming and a Mixed Numerical-Symbolic Penalty Formulation
,”
Mech. Mach. Theory
,
32
(
2
), pp.
161
174
.10.1016/S0094-114X(96)00037-7
3.
Etman
,
L. F. P.
,
Van Campen
,
D. H.
, and
Schoofs
,
A. J. G.
,
1998
, “
Design Optimization of Multibody Systems by Sequential Approximation
,”
Multibody Syst. Dyn.
,
2
(
4
), pp.
393
415
.10.1023/A:1009780119839
4.
Gonçalves
,
J. P. C.
, and
Ambrósio
,
J. A. C.
,
2005
, “
Road Vehicle Modeling Requirements for Optimization of Ride and Handling
,”
Multibody Syst. Dyn.
,
13
(
1
), pp.
3
23
.10.1007/s11044-005-2528-5
5.
Thoresson
,
M.
,
Uys
,
P.
,
Els
,
P.
, and
Snyman
,
J.
,
2009
, “
Efficient Optimisation of a Vehicle Suspension System, Using a Gradient-Based Approximation Method, Part 1: Mathematical Modelling
,”
Math. Comput. Modell.
,
50
(
9–10
), pp.
1421
1436
.10.1016/j.mcm.2009.07.011
6.
García de Jalón
,
J.
,
Callejo
,
A.
, and
Hidalgo
,
A. F.
,
2012
, “
Efficient Solution of Maggi's Equations
,”
ASME J. Comput. Nonlinear Dyn.
,
7
(
2
), p.
021003
.10.1115/1.4005238
7.
Ambrósio
,
J. A. C.
,
Neto
,
M. A.
, and
Leal
,
R. P.
,
2007
, “
Optimization of a Complex Flexible Multibody Systems With Composite Materials
,”
Multibody Syst. Dyn.
,
18
(
2
), pp.
117
144
.10.1007/s11044-007-9086-y
8.
Chang
,
C. O.
, and
Nikravesh
,
P. E.
,
1985
, “
Optimal Design of Mechanical Systems With Constraint Violation Stabilization Method
,”
ASME J. Mech. Des.
,
107
(
4
), pp.
493
498
.10.1115/1.3260751
9.
Haug
,
E. J.
,
1987
, “
Design Sensitivity Analysis of Dynamic Systems
,”
Computer Aided Optimal Design: Structural and Mechanical Systems
,
Springer
,
Berlin, Germany
, pp.
705
755
.
10.
Krishnaswami
,
P.
, and
Bhatti
,
M. A.
,
1984
, “
A General Approach for Design Sensitivity Analysis of Constrained Dynamic Systems
,”
ASME
Paper No. 84-DET-132.10.1115/84-DET-132
11.
Serban
,
R.
, and
Freeman
,
J. S.
,
1996
, “
Direct Differentiation Methods for the Design Sensitivity of Multibody Dynamic Systems
,”
The 1996 ASME Design Engineering Technical Conferences and Computers in Engineering Conference
, Irvine, California, August 18–22, pp.
18
22
.
12.
Maly
,
T.
, and
Petzold
,
L. R.
,
1996
, “
Numerical Methods and Software for Sensitivity Analysis of Differential-Algebraic Systems
,”
J. Appl. Numer. Math.
,
20
(
1–2
), pp.
57
79
.10.1016/0168-9274(95)00117-4
13.
Dopico
,
D.
,
Sandu
,
A.
, and
Sandu
,
C.
,
2014
, “
Direct and Adjoint Sensitivity Analysis of ODE Multibody Formulations
,”
ASME J. Comput. Nonlinear Dyn.
,
10
(
1
), p.
011012
.10.1115/1.4026492
14.
Wang
,
X.
,
Haug
,
E. J.
, and
Pan
,
W.
,
2005
, “
Implicit Numerical Integration for Design Sensitivity Analysis of Rigid Multibody Systems
,”
Mech. Des. Struct. Mach.
,
33
(
1
), pp.
1
30
.10.1081/SME-200045801
15.
Brüls
,
O.
, and
Eberhard
,
P.
,
2008
, “
Sensitivity Analysis for Dynamic Mechanical Systems With Finite Rotations
,”
Int. J. Numer. Methods Eng.
,
74
(
13
), pp.
1897
1927
.10.1002/nme.2232
16.
Banerjee
,
J.
, and
McPhee
,
J.
,
2013
, “
Symbolic Sensitivity Analysis of Multibody Systems
,”
Multibody Dynamics, Computational Methods in Applied Sciences
, Vol.
28
,
J.-C.
Samin
, and
P.
Fisette
, eds.,
Springer
,
Amsterdam, The Netherlands
, pp.
123
146
.
17.
Griewank
,
A.
, and
Walther
,
A.
,
2008
,
Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation
,
SIAM
, Philadelphia, PA.
18.
Callejo
,
A.
,
Narayanan
,
S. H. K.
,
García de Jalón
,
J.
, and
Norris
,
B.
,
2014
, “
Performance of Automatic Differentiation Tools in the Dynamic Simulation of Multibody Systems
,”
Adv. Eng. Software
,
73
, pp.
35
44
.10.1016/j.advengsoft.2014.03.002
19.
Pacejka
,
H.
,
2005
,
Tyre and Vehicle Dynamics
,
Elsevier
, Oxford, UK.
20.
Callejo
,
A.
,
2013
, “
Dynamic Response Optimization of Vehicles Through Efficient Multibody Formulations and Automatic Differentiation Techniques
,” Ph.D. thesis, Universidad Politécnica de Madrid, Madrid, Spain.
21.
Gutiérrez-López
,
M. D.
,
Callejo
,
A.
, and
García de Jalón
,
J.
,
2012
, “
Computation of Independent Sensitivities Using Maggi's Formulation
,”
The 2nd Joint International Conference on Multibody System Dynamics
, Stuttgart, Germany, May 29–June 1.
22.
García de Jalón
,
J.
, and
Bayo
,
E.
,
1994
,
Kinematic and Dynamic Simulation of Multibody Systems
,
Springer-Verlag
,
NY
.
23.
Walther
,
A.
, and
Griewank
,
A.
,
2010
, “
A Package for the Automatic Differentiation of Algorithms Written in C/C++
,” https://projects.coin-or.org/ADOL-C
24.
Mastinu
,
G.
,
Gobbi
,
M.
, and
Miano
,
C.
,
2006
,
Optimal Design of Complex Mechanical Systems—With Applications to Vehicle Engineering
,
Springer
,
Berlin, Germany
.
25.
Griffin
,
M. J.
,
2007
, “
Discomfort From Feeling Vehicle Vibration
,”
Veh. Syst. Dyn.
,
45
(
7–8
), pp.
679
698
.10.1080/00423110701422426
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