Indirect Vibration Sensing and Optimal Sensor Placement

The problems to estimate the response of a flexible structure using indirect sensors and to select the best possible locations for these measurements are addressed. The sensor placement problem and the indirect sensing problem are simultaneously approached by considering the Kalman filter. For linear systems exposed to Gaussian white process and measurement noise the Kalman filter provides the optimal estimate of the internal states. The state estimate can be used to map the measured response to the desired response of the structure. A sensor placement index is derived which addresses the statistical properties of the response estimate and a sensor set expansion procedure is formulated. The sensor of the candidate set that maximizes the performance of the Kalman filter is added to the selected set by recursion. This constitutes a computationally inexpensive but sub-optimal procedure. The method can be generalized to treat different types of sensors and response quantities in a straightforward manner. In particular the application to modal state tracking is illustrated. A numerical example which demonstrate the procedure is given. Comparisons between this sub-optimal procedure and the globally optimal sensor placement are made. Furthermore, the predictive ability of the method is satisfactory in the example.