Efficient Robust Optimization of Structures Subjected to Earthquake Load and Characterized by Uncertain Bounded System Parameters - Structural Seismic Design Optimization and Earthquake Engineering - page 108

Beck (2008) proposed an RDO procedure for
a base-isolation system under earthquake load
considering system parameter uncertainty. The
unconditional performance function was evaluated
through stochastic simulation. Guedri et al. (2009)
proposed a stochastic metamodel based approach
integrated with an RDO procedure to reduce the
cost of uncertainty analysis. In a recent study,
Marano et al. (2010) presented an RDO criterion
for a TMD system in seismic vibration control of
structures. Taflanidis (2010) presented an RDO
procedure of a linear dynamic system under
stochastic stationary excitation using simulation
based approach.
The review of currently available literature
reveals that the developments in the field of
RDO procedures have been taken place in three
distinct areas: (i) mathematical formulation of
RDO procedure as a SSO problem or deterministic
programming (Du, & Chen, 2000; Lee, & Park,
2001; Gunawan, & Azarm, 2005), (ii) solution
strategies (Du, Sudijianto, & Chen, 2004; Beyer,
& Sendhoff, 2007), and (iii) assessment of robust-
ness (Huang, & Du, 2007). The literature on RDO
procedures largely indicates that the applications
of RDO procedures in dynamics is lesser compared
to its applications in static. Moreover, in many
such applications, the dynamic load is consid-
ered to be deterministic in nature. It is generally
observed that the existing RDO formulations put
equal importance to each individual gradient of
the performance function and constraints. But, it
is well-known to the structural reliability com-
munity that all the gradients of a performance
function are not of equal importance (Gupta, &
Manohar, 2004; Haldar, & Mahadevan, 2000).
In fact, when a large numbers of DVs and DPs
are involved in a structural reliability analysis
problem, the dominant parameters having rela-
tively stronger influence on the reliability are
identified by using the relative importance of the
gradients. The concept has been successfully used
in the reduction of number of random variables
in large scale reliability analysis problems. Thus,

it is intuitively expected that the importance of
the individual gradient should also provide use-
ful information to measure the robustness of the
performance of a design and the concept can be
applied in the RDO procedure. In this regard,
it is of worth mentioning that most of the engi-
neering design problems are strongly based on
computationally expensive complex computer
code and numerical analysis. For a large-scale
system design, a preferable strategy is to utilize
the metamodelling technique to approximate the
implicit performance functions and constraints
(Jurecka, Ganser, & Bletzinger, 2007). However,
the accuracy of the metamodel based optimization
approach relies on how accurate the response sur-
face method ( RSM ) is in capturing the performance
variations during the iteration cycles of a typical
numerical optimization procedure (Jin, Chen, &
Simpson, 2001). Generally, the RSM is based on
the least-squares method ( LSM ) which is primar-
ily a global approximation of scatter position data
(Myers, & Montogmery, 1995). It is well-known
that the LSM is one of the major sources of error
in the response approximation by the RSM . The
moving least-squares method ( MLSM ), basically
a local approximation approach is found to be
more efficient in this regard (Kim, Wang, & Choi,
2005). However, the studies addressing the RDO
of structure using the MLSM based metamodel-
ling technique is observed to be scarce than the
applications of the MLSM addressing the RBDO
or the DDO procedures.
The focus of the present chapter is on an
improved RDO strategy for structures subjected
to stochastic earthquake load and characterized
by UBB type DVs and DPs . The formulation is
proposed in the framework of MLSM based adap-
tive RSM . The basic idea of the proposed RDO
approach is to improve the robustness of the per-
formance function using a new dispersion index,
which utilizes the weight factors proportional to
the importance of each gradient of the performance
function. The same concept is also applied to the
constraints. The repeated computations of the