Performance-Based Seismic Design - Structural Seismic Design Optimization and Earthquake Engineering - page 47

Figure 13. BWBN model regression for cyclic displacement history

the responses over the set of secondary
variables. These means and standard de-
viations are then represented by neural
networks with the main variables as the
input. This approach facilitates the use of
simulation in the estimation of the non-
performance probabilities, at a great com-
putational saving.

mance criteria. The Chapter has described
a search-based algorithm for the optimiza-
tion, not requiring the calculation of gra-
dients. The optimization requires initial
values for the design parameters, and the
work has considered initial values to be
those from a preliminary design. Further,
the Chapter considered the sensitivity of
the optimal solution to the initial condi-
tions, with the conclusion that the final
result for total cost was essentially insensi-
tive, but that the corresponding individual
design parameters could be quite different.

• The reliability indices β associated with

the performance criteria are thus calculated
in terms of the design parameters, and neu-
ral networks for the reliabilities are trained
with those parameters as input.

• The design optimization is carried out for

minimum total cost with minimum reli-
ability constraints for each of the perfor-

Table 11. Reliability results and comparison be-
tween hysteretic representation approaches

Table 10. Statistical data for the intervening
variables

Limit
displacement,
capacity factor λ

Reliability index β

Hysteresis: Finite
Element

Hysteresis:
BWBN

Standard
Deviation

Variable Distribution Mean

0.1 -0.143 0.716

a G (m/sec 2 ) Lognormal 1.0 0.6

0.2 1.097 1.724

ω S (rad/sec) Normal 4π π

0.4 2.509 2.379

T (sec) Normal 12 2

0.6 3.197 2.675

M (kN.
sec 2 /m)

Normal 150 15

0.8 3.730 2.892

D R Normal 0.5 0.1 1.0 4.243 3.082