A Technique for Placing Few Sensors on a Building for Complete Modal Identification

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Satisfactory calibration between a building and its numerical model can be achieved through system identification and model updating methods using responses recorded on the structures during seismic excitation or ambient vibration conditions. Due to economic considerations, the responses are commonly recorded at only few locations on the building. The identification of structural parameters of a general torsionally-coupled shear building with varying story stiffness and mass on each story requires response characteristics that may not be captured when only a few responses are recorded. This paper describes a method that uses interpolation techniques to increase the number of available responses for system identification for shear buildings subjected to base excitation. The responses at non-instrumented floor levels of building are reconstructed by interpolating using spline shape function. The recorded and reconstructed responses are used in a parameter identification algorithm to extract the modal properties of the building (natural frequencies, damping ratios and mode shapes). A rigorous analysis procedure that extends the spline shape function method to shear building for identifying effective locations of sensors is presented. The error in the reconstructed responses are defined by global minimax error and used in identifying locations of sensors on the building. The most suitable sensor locations for recording responses are found to be most linearly independent degrees-of-freedom in the structure as defined by the QR-decomposition of modal matrix of the building. The comparison of identified modal parameters and reconstructed responses shows good agreement with the corresponding exact value.