# Sensor Placement on a Cantilever Beam Using Observability Gramians

arXiv: https://arxiv.org/abs/2501.01726 · HTML: https://mlsanity.com/paper/2501.01726/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jan 2025.

## Built on by (most cited first, 2 of 2)

- [Adaptive Diffusion Posterior Sampling for Data and Model Fusion of Complex Nonlinear Dynamical Systems](https://mlsanity.com/paper/2603.12635/) (2026)
- [Observability Conditions and Filter Design for Visual Pose Estimation via Dual Quaternions](https://mlsanity.com/paper/2605.02054/) (2026)

## Abstract (arXiv)

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.