# UNIVERSITY OF VERMONT

# SCHOOL OF ENGINEERING

## Civil Engineering Seminar Series

**Presents:
**

**
Dr. Dionisio Bernal**

Civil and Environmental Engineering Department,

Center for Digital Signal Processing, Northeastern University, Boston MA 02115

**Abstract
****
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.

**Brief Bio:**

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.

September 20^{th}

12:50-1:40 pm

Perkins 101