Shape estimation of distorted flexible structures

The present work discusses the optimal placement of sensors in truss structures in order to obtain best possible information regarding the distortions of the structure. The estimation goal is to reconstruct the deformed shape of the structure, at the controlled degrees of freedom, from the sensor readings. A basic assumption is that the structure is subjected to a parametric disturbance field. We distinguish between disturbances which cause uniform or arbitrary distortions of the structure, and disturbances which cause structured distortions. Uniform distortions can be construed as white noise, that is, distortions which have no characteristics. Structured distortions are chromatic, they have some characteristics which can be helpful in estimating the shape. Although the disturbance in either case is random it is assumed that its magnitude is confined to a hyper sphere. The estimator is based on the least squares method, hence the estimated shape is the one with least RMS displacement for the given sensor readings. To evaluate the performance of each set of sensors a measure is derived based on the concept of the worst case distortion. The measure is the largest possible error between the estimated and the actual displacements, at the CDOF. For small number of sensors all possible arrangements can be generated and compared. Larger trusses with a moderate number of sensors generate prohibitively large number of possible configurations, hence heuristic search techniques are employed. The theory has been applied to 2D and 3D flexible trusses. Results show that for reasonable shape estimation a relatively large number of sensors is needed. It is also shown that when using sensors which measure mainly the distortions of the controlled degrees of freedom, significant improvements in the shape estimation can be obtained.