Optimal Placement of Controller for Seismic Structures - Design Optimization of Active and Passive Structural Control Systems - page 6

Table 1. The sequential search method

• The Sequential Search algorithm (SS)

• The Worst-Out-Best-In algorithm (WOBI)

Step by Step Procedure
Step 1: For the placement of the first damper, set k=1.
Step 2: Select stiffness k d and damping coefficients c d .
Step 3: Assemble the vector Ivec(k) that containing optimal
locations. Set it null.
Step 4: Assemble the damper matrix G (set G = 0)
Step 5: For distinct locations, evaluate the objective function if
at each of the (n-k-1) story units; for repeated locations,
evaluate the objective function if at each of the n story units.
Step 6: The if th story unit with the best value of objective
function is identified as the optimal location for the first
damper, so add it to the list of optimal locations.
Step 7: Set Ivec(k)= I.
Step 8: Set k=k+1.
Step 9: if k>r, stop; if k<r go to step 4.

• The Exhaustive-Single-Point-Substitution

algorithm (ESPS)

The Sequential Search
(SS) Algorithm

The method consists of placing r dampers in n
story units. It starts by placing the first damper
in a particular story unit and evaluating the cor-
responding objective function. This process is
repeated for all story units and the story unit,
which corresponds to the best objective function,
is selected as the optimal location for the first
damper (Table 1). After that the first damper is
located in its optimal location, this procedure is
repeated for all remaining dampers (Figure 1).
This method can be used for two types of
damper placement strategies:

for each of the r configurations of (r-1) dampers,
obtained by removing one damper from I 0 . The
configuration of (r-1) dampers, obtained by elimi-
nating the worst damper, is denoted by I 1 . Then, the
removed damper is placed in the (n-r) story units
and the performance index is evaluated for every
configuration. The configuration corresponding
to the optimal objective function is denoted by I 2 .
This procedure is an iterative one, and evaluations
are continued till no improvement in the objective
function is possible (Figure 2). In WOBI search,
a total of r+(n-r)=n evaluations of the objective
function are required in each iteration to find
the optimal locations (for the case of distinctive
location strategy). The method is summarized in
a step by step procedure in Table 2.

1. Distinctive Locations: With this strategy
only one damper can be located in a story
unit, while the second damper can be placed
in the rest of (n-1) story units. So the required
number of evaluations for the objective
function is {n×r-[r×(r-1)/2]}.
2. Repeated Locations: With this strategy,
more than one damper can be located in
a story unit, while the second damper can
be placed in all story units. So the required
number of evaluations for the objective
function is n×r.

The Worst-Out-Best-In
(WOBI) Search Algorithm

The Exhaustive-Single-Point
Substitution (ESPS) Search
Algorithm

This method starts with an initial configuration of
r dampers, denoted by I 0 , and the corresponding
objective function is denoted by if 0 . Generally,
I 0 corresponds to the configuration obtained by
either the sequential search method (SS) or any
given pre-design method. In the WOBI search
algorithms the objective function if is calculated

The ESPS method, like the WOBI method, starts
with an initial configuration of r dampers, denoted
by I 0 , and the corresponding objective function
is denoted by if 0 . Generally I 0 corresponds to the
configuration obtained by either the sequential