In this paper we focus on the optimal placement of sensors for state estimation-based continuous health monitoring of structures using three approaches.  The first aims to minimize the static estimation error of the structure deflections, using the linear stiffness matrix derived from a finite element model.  The second approach aims to maximize the observability of the derived linear state space model. The third approach aims to minimize the dynamic estimation error of the deflections using a Linear Quadratic Estimator.  Both nonlinear mixed-integer and relaxed convex optimization formulations are presented.  A simple search-based optimization implementation for each of the three approaches is demonstrated on a model of the long-span New Carquinez Bridge in California.

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