Investigation of filtering techniques applied to the dynamic shape estimation problem

This paper investigates the use of filtering techniques, such as the Kalman filter, to perform dynamic shape estimation of structures. Existing dynamic shape estimation techniques use static estimation techniques at each time step. This approach has been shown to be unsatisfactory, since aliasing of the higher modes, which is generally not seen in the static case, occurs strongly in the dynamic case. In many cases aliasing produces signal to noise ratios significantly greater than unity. Two approaches are proposed. The first approach improves upon existing techniques by using low-pass filters that are designed to roll-off after the natural modes that contribute significantly to the deformation of the structure, reducing effect of high-frequency noise and aliasing. The second approach uses a Kalman filter to sift out the desired low-frequency modes, since they contribute most to the displacements, while treating the higher modes as a component of the noise present in the system. Unlike static estimation techniques, the Kalman filter-based technique easily allows consideration of a number of modes larger than the number of sensors and takes into account the measurement errors. Numerical simulations were conducted to compare various dynamic estimation techniques and the results show that the Kalman filtering technique can reduce the error from 1000% down to less than 1% for an ideal cantilever beam. Experimental data, susceptible to modeling and sensing errors, show that the proposed methods result in significant improvement over existing techniques.