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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.

The objective of this research was to predict the influence of non-uniform temperature distribution on solar sail topology and the effect of such topology variations on sail performance (thrust, torque). Specifically considered were the thermal effects due to onorbit attitude control maneuvers. Such maneuvers are expected to advance the sail to a position off-normal to the sun by as much as 35 degrees; a solar sail initially deformed by typical pre-tension and solar pressure loads may suffer significant thermally induced strains due to the non-uniform heating caused by these maneuvers. This on-orbit scenario was investigated through development of an automated analytical shape model that iterates many times between sail shape and sail temperature distribution before converging on a final coupled thermal structural affected sail topology. This model utilizes a validated geometrically non-linear finite element model and a thermal radiation subroutine. It was discovered that temperature gradients were deterministic for the off-normal solar angle cases as were thermally induced strains. Performance effects were found to be moderately significant but not as large as initially suspected. A roll torque was detected, and the sail center of pressure shifted by a distance that may influence on-orbit sail control stability. Nomenclature A = Flat-sail projected area for one quadrant, 75.6 m

The Videogrammetric Model Deformation (VMD) technique, developed at NASA Langley Research Center, was recently used to measure displacements and local surface angle changes on a static aeroelastic wind-tunnel model. The results were assessed for consistency, accuracy and usefulness.Vertical displacement measurements and surface angular deflections (derived from vertical displacements) taken at no-wind/no-load conditions were analyzed. For accuracy assessment, angular measurements were compared to those from a highly accurate accelerometer. Shewhart's Variables Control Charts were used in the assessment of consistency and uncertainty. Some bad data points were discovered, and it is shown that the measurement results at certain targets were more consistent than at other targets. Physical explanations for this lack of consistency have not been determined. However, overall the measurements were sufficiently accurate to be very useful in monitoring wind-tunnel model aeroelastic deformation and determining flexible stability and control derivatives. After a structural model component failed during a highly loaded condition, analysis of VMD data clearly indicated progressive structural deterioration as the wind-tunnel condition where failure occurred was approached. As a result, subsequent testing successfully incorporated near-real-time monitoring of VMD data in order to ensure structural integrity. The potential for higher levels of consistency and accuracy through the use of statistical quality control practices are discussed and recommended for future applications.

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