Optimal sensor placement through expansion of static strain measurements to static displacements

Optimal sensor placement is used to establish the optimal sensor quantity and layout. In this study, the minimum quantity and locations of measurement sensors were assumed to satisfy the constraint conditions of the optimal sensor placement. A set of strain data in a truss structure was expanded to another set of displacements corresponding to the entire degrees of freedom from the relationship between the strain and displacement. It indicates to reduce the number of sensors because the strain depends on the displacements in a finite element model. The damaged truss element was traced using the expanded data that satisfied the prescribed constraints. The proposed optimal sensor placement method has a merit to explicitly determine the optimal sensor locations without any numerical scheme and statistical methods. The method was applied to the damage detection of a single-damaged truss structure. It was shown that the optimal sensor placement method depended on the sensor layout irrespective of the same quantity of sensors. In addition, a numerical example was used to compare sensitivities to damage detection based on the sensor placement and the existence of external noise contained in the measurement data.