Life-cycle Cost Optimal Design of Passive Dissipative Devices for Seismic Risk Mitigation
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The cost effective performance of structures has long
been recognized to be an important topic in the design
of civil engineering systems. This design approach
requires proper integration of (i) methodologies for
treating the uncertainties related to natural hazards
and to the structural behavior over the entire lifecycle
of the building, (ii) tools for evaluating the
performance using socioeconomic criteria, as well as
(iii) algorithms appropriate for stochastic analysis and
optimization.
A complete probabilistic framework is presented in
this paper for detailed estimation and optimization of
the life-cycle cost of earthquake engineering systems.
The focus is placed on the design of passive dissipative
devices. The framework is based on a knowledge-based
interpretation of probability (Jaynes, 2003),
which leads to a realistic framework for formulating
the design problem, and on an efficient novel approach
to stochastic optimization problems (Taflanidis and
Beck, 2008). The latter facilitates an efficient solution
of this design problem and thus allows for consideration
of complex models for describing structural
performance.
A comprehensive methodology is initially discussed
for earthquake loss estimation; this methodology uses
the nonlinear time-history response of the structure
under a given excitation to estimate the damages in
a detailed, component level. A realistic probabilistic
model is then presented for describing the ground
motion time history for future earthquake excitations.
This model establishes a direct link between the probabilistic
seismic hazard description of the structural
site and the acceleration time history of future ground
motions. In this setting, the life-cycle cost is given
by an expected value over the space of the uncertain
parameters for the structural system, performance
evaluation and excitation models. Because of the complexity
of these models, calculation of this expected
value by means of stochastic simulation techniques is
adopted. This approach, though, involves an unavoidable
estimation error and significant computational
cost, features which make the associated optimization
challenging. An efficient framework, consisting
of two stages, is presented for the optimization in such
stochastic design problems. The first stage implements
a novel approach, called-Stochastic Subset Optimization
(SSO), for efficiently exploring the sensitivity of
the objective function to both the design variables as
well as the model parameters. Using a small number
of stochastic analyses SSO iteratively identifies a
subset of the original design space that has high plausibility
of containing the optimal design variables and
additionally consists of near-optimal solutions. The
second stage, if needed, adopts some other stochastic
optimization algorithm to pinpoint the optimal design
variables within that subset. All information available
from the first stage is exploited in order to improve the
efficiency of the second optimization stage.
An example is presented that considers the
retrofitting of a four-story reinforced concrete office
building with viscous dampers. Complex system,
excitation and performance evaluation models are
considered, that incorporate all important characteristics
of the true system and its environment into
the design process. The results illustrate the capabilities
of the proposed framework for improving the
structural behavior in a manner that is meaningful to
its stakeholders (socio-economic criteria), as well as
its capabilities for computational efficiency and the
treatment of complex analysis models.