Dr. Dionisio Bernal
Civil and Environmental Engineering Department,
Center for Digital Signal Processing, Northeastern University, Boston MA 02115
Input Reconstruction in Linear Systems
This seminar examines the problem of identifying the sampled histories of dynamic forces acting at a number of predetermined locations and in known directions from observations at a limited number of coordinates. The first item examined is the question of identifiability. After illustrating the limitation of finite dimensional models regarding dead time it is shown that the relevant issue for identifiability is the amount of information about the inputs that is contained in the outputs. A procedure to compute this information in the case where the noise in the measurements can be assumed jointly Gaussian is shown and it is used to decide on the optimal prediction lag of a reconstruction algorithm designated as the Segmented Deconvolution Reconstruction (SDR) scheme. Analysis of the information content in the frequency domain sheds light into the structure of conditioning in frequency and on the effect of the type of measurement on the attainable accuracy. The SDR algorithm applies equally in collocated and non-collocated cases and, within the assumptions of the finite dimensional model, is exact. The seminar also shows how the "blind manipulation" of the equations of finite dimensional representations of linear systems has led to algorithms, usually referred to as simultaneous state and input estimators that propose to do the impossible, namely: to estimate inputs from measured outputs with one time step delay, independently of the distance between inputs and outputs and independently of the time step size.
Dionisio Bernal is a Professor of the Civil and Environmental Engineering Department and a member of the Center for Digital Signal Processing at Northeastern University, Boston. He is the recipient of the Moisseiff Award from the American Society of Civil Engineers (ASCE) for his work in dynamic instability of buildings subjected to earthquakes and of the Hayes and Martin Essigmann Awards from Northeastern University for excellence in Teaching and Research. His research spans the areas of earthquake engineering, structural dynamics and computational techniques.