Sensor Placement on a Cantilever Beam Using Observability Gramians

TL;DR

This paper develops observability Gramian tools for continuum systems and applies them to optimize sensor placement on a cantilever beam, demonstrating improved estimation accuracy over random placement.

Contribution

It introduces analytical and empirical observability Gramian methods for continuum systems and applies them to optimal sensor placement on a cantilever beam.

Findings

Optimal sensor placement improves estimation accuracy.

Analytical observability methods outperform random placement.

Error covariance analysis validates the effectiveness of the proposed techniques.

Abstract

Working from an observability characterization based on output energy sensitivity to changes in initial conditions, we derive both analytical and empirical observability Gramian tools for a class of continuum material systems. Using these results, optimal sensor placement is calculated for an Euler-Bernoulli cantilever beam for the following cases: analytical observability for the continuum system and analytical observability for a finite number of modes. Error covariance of an Unscented Kalman Filter is determined for both cases and compared to randomly placed sensors to demonstrate effectiveness of the techniques.