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heuristic placement method. This method, the
Sequential Search Algorithm (SSA), was consid-
ered an advancement in the field because of its
practicality. Zhang and Soong (1992) compared
SSA to Uniform damping, concluding that with
SSA, 2-5 dampers were saved for a 10-story
structure with viscoelastic dampers using drift as
the performance criterion. Additional performance
objectives, such as absolute accelerations, were
not considered, and a relatively small amount of
damping (10% effective damping ratio) was se-
lected. Other researchers verified the SSA method
for viscoelastic dampers and a shear-frame model
(Shukla and Datta, 1999) and for torsional effects
of a three-dimensional model (Wu et al., 1997).
An evolution of the SSA method was the
Simplified Sequential Search Algorithm (SSSA)
(Lopez-Garcia, 2001), which sought to further
simplify the method for passive devices by de-
creasing the computational-effort of determining
optimal locations and simulating stochastic ground
motions. It claimed simplicity and practicality over
existing methods due to its sequential procedure,
use of tools familiar to designers, and inherent
consideration of discrete damper sizes.
Limitations of the original SSSA study include
the use of few ground motions, small unrealistic
damping levels (less than 10% effective damping
ratio with dampers) for comparing SSSA to other
methods, and the use of example structures and
damper placement distributions from previous
researchers. The last limitation implies that the
placement methods compared to SSSA were not
followed in full and therefore, usability of the
methods could not be adequately compared. The
method's dependency on specific ground mo-
tions and proven effectiveness limited to linear
structures were two inherent limitations of the
technique. However, Lopez-Garcia and Soong
(2002) confirm that the sensitivity of the SSSA
damper distribution to ground motion characteris-
tics decreases with increasing levels of damping.
Minor differences were found in SSSA damper
distributions for four different ground motions
with 18% damping as compared to much larger
discrepancies in distribution when using 6% damp-
ing for the same structure and ground motions.
An alternative stochastic approach is the use
of genetic algorithms. These are evolutionary
techniques specifically applied to combined
global optimisation problems (Pintér 2008). The
algorithm evolves based on user-provided fitness
functions; new generations 'reproduce' until some
termination criterion is satisfied. Examples of
application to the damper placement problem
include Movaffaghi and Friberg (2006), who pro-
posed optimisation using genetic algorithms with
discrete variables (using the IDESIGN software
interfaced with ABAQUS). Singh and Moreschi
(2002) developed a genetic algorithm method to
optimally place and size viscous and viscoelastic
dampers. The method was demonstrated for vari-
ous linear dampers and linear, shear and torsional
structures and assessed for interstory drifts, floor
accelerations, and shear forces. Although the ge-
netic algorithm is a powerful optimisation method,
its main disadvantage is high computational time.
Deterministic Methods
Many analytical optimal placement methods have
been proposed, including methods based on the
principles of optimal control theory, gradient-
based search methods, and an analysis/redesign
method.
Gluck et al. (1996) adapted optimal control
theory (OCT) to the damper placement problem.
OCT is used to minimise the performance objec-
tive by optimising the location of linear passive
devices. Since passive dampers cannot provide
feedback in terms of optimal control gains, three
approaches (response spectrum approach, single
mode approach, and truncation approach) are pro-
posed to remove the off-diagonal state interactions
within the gain matrix and allow approximation of
floor damping coefficients. Combination of these
methods with OCT and passive devices achieves
an equivalent effect compared to active control,
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