- This event has passed.
EBE Grad Seminar Weekly Talk: On a Mechanical Interpretation of the Kalman Filter
September 27, 2019 @ 1:00 pm - 2:00 pm
Presenter: Dr. Eric M. Hernandez, CEE-UVM
Title: On a Mechanical Interpretation of the Kalman Filter
Abstract: The Kalman filtering, also known as linear quadratic estimation (LQE), is an algorithm that uses a series of measurements observed over time, containing statistical noise and other inaccuracies, and produces optimal estimates of unknown/hidden variables (states). The filter/observer is named after Rudolf E. Kalman, one of the primary developers of its theory. The Kalman filter is one of the most celebrated algorithms of the 20th century and it has found application in many fields of science, technology, engineering and finance.
This seminar presents a derivation of the Kalman filter which allows the filter to be approximated as a surrogate mechanical system. The resulting estimator is a modified version of the system of interest driven in real-time by forces which are proportional to the measurements. The response of the estimator system to the measurement-proportional forces constitutes an estimate of the state variables of interest. The statistical properties of the state error can also be derived using the proposed analogy. This interpretation of the Kalman filter is known as a Model-based Observer (MBO). In addition to being an interesting mathematical curiosity, this mechanical interpretation of the Kalman filter is endowed with several implementation advantages which will be discussed in the seminar. The presentation will focus on applications of the MBO to structural health monitoring, and in particular, fatigue monitoring of wind excited structures and tall buildings subject to earthquake-induced excitations. The effectiveness of the MBO will be illustrated in the context of simulations, lab experiments and large-scale structures.
Speaker’s Bio:
Title: On a Mechanical Interpretation of the Kalman Filter
Abstract: The Kalman filtering, also known as linear quadratic estimation (LQE), is an algorithm that uses a series of measurements observed over time, containing statistical noise and other inaccuracies, and produces optimal estimates of unknown/hidden variables (states). The filter/observer is named after Rudolf E. Kalman, one of the primary developers of its theory. The Kalman filter is one of the most celebrated algorithms of the 20th century and it has found application in many fields of science, technology, engineering and finance.
This seminar presents a derivation of the Kalman filter which allows the filter to be approximated as a surrogate mechanical system. The resulting estimator is a modified version of the system of interest driven in real-time by forces which are proportional to the measurements. The response of the estimator system to the measurement-proportional forces constitutes an estimate of the state variables of interest. The statistical properties of the state error can also be derived using the proposed analogy. This interpretation of the Kalman filter is known as a Model-based Observer (MBO). In addition to being an interesting mathematical curiosity, this mechanical interpretation of the Kalman filter is endowed with several implementation advantages which will be discussed in the seminar. The presentation will focus on applications of the MBO to structural health monitoring, and in particular, fatigue monitoring of wind excited structures and tall buildings subject to earthquake-induced excitations. The effectiveness of the MBO will be illustrated in the context of simulations, lab experiments and large-scale structures.
Speaker’s Bio:
Dr. Eric M. Hernandez holds the Gregory N. Sweeny Green & Gold Professorship in Civil Engineering at the University of Vermont. Areas of expertise include direct and inverse problems in structural dynamics, structural health monitoring, Bayesian reliability and decision-making under uncertainty. His research has been funded by the National Science Foundation, NASA and the Vermont Agency of Transportation. Prior to joining academia, Dr. Hernandez practiced Structural Engineering in the United States and abroad. His experience spans seismic analysis and design of nuclear facilities, buildings, bridges and other structures. For more information visit www.emhernandez.com
Each week, the graduate students in EBE engage with thought leaders around relevant, compelling topics. Speakers and locations will be posted on an ongoing basis.
