Life-cycle Cost Optimal Design of Passive Dissipative Devices for Seismic Risk Mitigation

Abstract

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.

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