Multi-Objective NSGA-II Optimization for Mitigating High Frequency Transient Vibrations in a 5-DOF Vehicle Model
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Abstract
Ride comfort in ground vehicles is governed not only by the steady-state response of the
suspension to road excitation but also by transient, high-frequency oscillations arising from the system's
homogeneous (free-vibration) response. This study was conducted through comprehensive numerical
simulation to formulate suspension design as a multi-objective optimization problem. A five degree of
freedom (5-DOF) lumped parameter vehicle model captures body heave, pitch, and unsprung mass
dynamics. Seven suspension and seat design variables are optimized with the Non-dominated Sorting
Genetic Algorithm II (NSGA-II) against two objectives: (i) the root mean squared seat acceleration over
an 8-second simulation window, and (ii) a frequency-weighted measure of the damped natural
frequency components above 5 Hz, extracted from the transient response via windowed Fourier
analysis. The framework is evaluated across a range of forcing frequencies under two deterministic
time-varying road inputs: an isolated double bump and a periodic pulse train. NSGA-II returns a well
distributed Pareto front, giving designers an explicit trade-off between overall ride comfort and rapid
attenuation of high-frequency transients. Solutions selected purely for minimum seat acceleration at the
nominal 1 Hz forcing frequency degrade sharply as the forcing frequency increases; solutions that also
account for the high-frequency objective retain stable performance and often achieve lower seat
acceleration than the single-objective optimum. These results indicate that jointly minimizing the
homogeneous high-frequency response alongside steady-state seat acceleration yields robust
suspension designs under fluctuating operational frequencies.
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