Geology Reference
In-Depth Information
The RDO Method: Developments
index expressed in terms of the mean value of the
performance function (obtained by the so called
RBDO
approach) as well as its dispersion due to
uncertainty. Thereby, a design configuration of the
structure can be achieved so that the performance
objective is less sensitive to the variations due to
system parameter uncertainty. Furthermore, the
RBDO
of structure, based on a probabilistic de-
scription of uncertain parameters attains its limita-
tion when sufficient reliable data are not available
for describing the system parameter uncertainty
of a real life system. In fact, often a probabilistic
description of uncertainty arising from insufficient
information is warned in order to incorporate our
partial knowledge about the system. A preferable
approach is to model the system parameters as
uncertain but bounded (
UBB
) type. In such a case,
the
RDO
approach becomes an attractive alterna-
tive to the
RBDO
approach. The
RDO
approach
is fundamentally concerned with minimizing the
effect of uncertainty in the Design Variables (
DVs
)
(the specific system parameters designer needs
to optimize to achieve a desired performance)
and the Design Parameters (
DPs
) (which cannot
be controlled by the designer or are difficult and
expensive to control). The subject of the present
chapter is the
RDO
of structures under stochastic
load (earthquake to be specific) considering
UBB
type system parameters.
The concepts of
RDO
have been developed
independently in different scientific disciplines
and the developments in the recent past are note-
worthy as evident from the works of Park et al.
(2006); Beyer, & Sendhoff (2007). The limited
information on uncertainty is usually integrated
with a nondeterministic optimization framework
to obtain an
RDO
(Park, Lee, & Hwang, 2006).
This approach is often referred as sensitivity
based approach. There are various such
RDO
approaches adopted by different researchers e.g.
robust counterpart approach (Lewis, 2002), semi-
definite programming (Ben-Tal, & Nemirovski,
2002; Bertsimas, & Sim, 2004), worst case sensi-
tivity region concept (Gunawan, & Azarm, 2005),
minimization of sensitivity matrix (Al-Widyan, &
Angeles, 2005) etc. A new semi-analytical method
to calculate the sensitivity of stability boundary
for a system of delay differential equations was
presented by Kurdi et al. (2008). Guo et al. (2009)
proposed a bi-level programming technique us-
ing a semi-definite programming to solve
RDO
problem under non-probabilistic and non-convex
stiffness and load uncertainties. The study on
RDO
procedure in the field of stochastic dynamic
systems is comparatively a less attempted area
compared to the deterministic design optimization
(
DDO
) and the
RBDO
procedures. Hwang et al.
(2001) minimized the mean and the variance of
displacement at the first resonance frequency of
an automobile mirror considering system param-
eter uncertainty. Zang et al. (2005) reviewed the
applications of optimization of dynamic system
and presented an
RDO
procedure for a vibration
absorber considering mass and stiffness uncertain-
ties under deterministic sinusoidal load. Son and
Savage (2007) proposed a probabilistic design of
vibration absorber parameters to reduce the mean
as well the variance of dynamic performance
measure. Marano et al. (2008) investigated
RDO
solution for a tuned mass damper (TMD) system
in seismic vibration mitigation. Taflanidis and
BACKGROUND
To present the proposed
RDO
approach, it will be
informative to discuss the background of
RDO
of
structures with emphasis on optimization of sto-
chastic dynamic system. In doing so, the related
developments in the field of
RDO
are presented
first to justify the relevance of the present study.
Subsequently, the concept of conventional
RDO
approach, the
SSO
under earthquake load as-
suming deterministic system parameters and the
metamodelling based approximation of stochastic
dynamic responses are briefly presented.
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