Investigation of filtering techniques applied to the dynamic shapeestimation problem

Abstract

This paper investigates the use of filtering techniques, such as theKalman filter, to perform dynamic shape estimation of structures. Existingdynamic shape estimation techniques use static estimation techniques at eachtime step. This approach has been shown to be unsatisfactory, since aliasingof the higher modes, which is generally not seen in the static case, occursstrongly in the dynamic case. In many cases aliasing produces signal to noiseratios significantly greater than unity. Two approaches are proposed. Thefirst approach improves upon existing techniques by using low-pass filtersthat are designed to roll-off after the natural modes that contributesignificantly to the deformation of the structure, reducing effect ofhigh-frequency noise and aliasing. The second approach uses a Kalman filter tosift out the desired low-frequency modes, since they contribute most tothe displacements, while treating the higher modes as a component of the noisepresent in the system. Unlike static estimation techniques, the Kalmanfilter-based technique easily allows consideration of a number of modes largerthan the number of sensors and takes into account the measurement errors.Numerical simulations were conducted to compare various dynamic estimationtechniques and the results show that the Kalman filtering technique can reducethe error from 1000% down to less than 1% for an idealcantilever beam. Experimental data, susceptible to modeling and sensingerrors, show that the proposed methods result in significant improvement overexisting techniques.