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Long-term and continuous health monitoring of structures is of essential interest within the civil engineering communities due to the aging of infrastructures. Detect defects and monitor various physical or chemical parameters related to the health of the structures is vital for safety evaluation and health monitoring allowing for decision-making in terms of maintenance and retrofitting. Among the parameters of interest, the deflection is one of the most important parameters because the deflection limit is usually utilized as a control index of structures when subjected to potential external loads. However, it is not easy to have a real-time structural variations measurement because of the difficulties in measuring the deflection directly. Indeed traditional direct techniques, like dial indicator, level, and total station, have limited discrete points and are suitable only for short term monitoring. While newer whole field techniques, like accelerometer, microwave interferometer, GPS, connected pipe optoelectronic liquid level sensor, are developed for real time deformation measurement, but they need to install additional setup that causes extra costs and measurement data. An alternative approach for monitoring the deflection of the structures is based on an indirect measure such as the strain with attachable sensors and using proper transformation to estimate the displacement field. Along this line of argument, Fiber Bragg Gratings (FBGs) are good alternative to strain gauges and in the last years a demonstration of the deflection monitoring has already been carried out limiting the attention to one dimensional structures. Thus, in this paper, we extend and generalize the deflection estimation to a multilayer bidimensional structures by using FBG strain sensors and a displacement-strain transformation. In particular, several FBGs have been embedded in the structure within only a few optical fibers, thus avoiding the complex wiring typical of strain gauges. Then, from the strain measured by the FBGs, the curvature function has been evaluated as a polynomial function whit the coefficients obtained by least mean square; and the deflection is estimated by integrating twice the curvature function. Experimental results show good agreement with those directly measured by a dial. The proposed technique allows a real-time indirect structural monitoring solving the existing difficulties in measuring the deflection directly, and can be applied to small as well large structure. Furthermore, it is crucial in high energy physics, where particle bidimensional detectors have to measure the position of the incoming radiation with a resolution of few tens of microns, and detectors deflection directly influences this measurements.
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