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Adequate sensor placement plays a key role in such fields as system identification, structural control, damage detection, and structural health monitoring (SHM) of large-scale civil infrastructures. Many optimal sensor placement (OSP) methods have been developed for general optimized solution searches. Due to the limitations of equipment facilities and cost, the number of sensors to be installed in a structure is relatively few. It is very important to determine the necessary number of sensors to be installed and where to deploy these sensors. Taking into account energy attenuate during the signal propagation, combined with classic reverberation matrix method, a two-step method is proposed to determine the sensors arrangement using the scattering matrix in this paper. First, calculate the utmost distance of wave propagation on a special structure by the principle of elastic wave propagation and determine the preliminary number of sensors; second, the utmost distance and number of sensors are applied to a sensor optimization algorithm named Effective Independence Driving-Point Residue method. In the bridge benchmark model case study, it shows the validity of proposed method under a special detection system.

We will use the Henstock (or generalized Riemann) approach to define the Stratonovich integral with respect to continuous semimartingale in 2 space. Our definition of Stratonovich integral encompasses the classical definition of Stratonovich integral.

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