Optimal Placement of Controller for Seismic Structures

Optimal Placement of Controller for Seismic Structures

Gian Paolo Cimellaro (Politecnico di Torino, Italy)
DOI: 10.4018/978-1-4666-2029-2.ch001
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The objective of this chapter is to evaluate different methodologies for the optimal placement and innovative design of passive energy dissipation systems which are being used to reduce vibrations of civil engineering structures subject to earthquakes. For large civil engineering structures it is necessary to install a sufficient number of dampers to achieve a reduction of the building response and the performance of these dampers depends on their location in the structures. The selection of few locations out of a large number of locations for the placement of passive dampers is typically a nonlinear constrained optimization problem. This problem can be solved either by simple heuristic search approaches which can be easily integrated in conventional design procedures used by practicing engineers dealing with damper-added structures, and they yield a solution which may be close to the optimal solution, but computationally expensive. Three different heuristic search strategies will be used to optimize four objective functions, and results will be compared for three different building typologies.
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The seismic response of structures subjected to earthquake excitations may be effectively reduced by incorporating any of various kinds of available passive energy dissipation devices (Soong and Dargush 1997). Numerous are the studies related to optimal placement and capacity of damping coefficient for linear multistory buildings.

Tsuji and Nakamura (1996) proposed an algorithm that finds the optimal story stiffness distribution and the optimal damper distribution for a shear building model subjected to a set of spectrum-compatible earthquakes, but it requires high computational afford because it is necessary to run dynamic analysis and include artificial constraints like the upper bound of the damping coefficients. Nakamura et al. (1996) found a method for evaluating an ordered set of stiffness design variables of an elastic shear type building with an ordered set of damping coefficients via an inverse problem approach, under the assumption that the ratio between the mean maximum interstory drift due to a spectrum compatible earthquake and the target specified value remains constant. Gluck, Reinhorn et al. (1996) suggested a method for the design of supplemental dampers and stiffness based on optimal control theory using a linear quadratic regulator (LQR) that minimizes a performance cost function, but the algorithm is valid under the assumption of white noise input and it is effective only for systems where the first mode effects are predominant.

Takewaki (1997) proposed a stiffness-damping simultaneous optimization procedure where the sum of mean square responses to stationary random excitations is minimized subjected to the constraints on total stiffness and damping capacity. It is a two-step optimization method where, in the first step, the optimal design is found for a specified value of total stiffness and damping, while in the second step the procedure is repeated for a set of total stiffness and damping capacity.

All methods mentioned above, even if they lead to an optimal damper configuration, are not practical, because they are not simple enough to be used routinely by practical engineers. An ideal method should be practical and capable of controlling the number of different damper sizes to be used. The method should be also efficient, in the sense that the resulting damper configuration (i.e., size and location of added dampers) minimizes the total amount of added damping necessary to reach a given performance objective.

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