Modal Analysis with Compressive Measurements

TL;DR

This paper introduces three compressive sensing frameworks for structural health monitoring that enable efficient vibration data collection and modal analysis without full signal reconstruction, reducing power consumption.

Contribution

It proposes novel CS-based methods for modal analysis in SHM that simplify data processing and provide theoretical measurement bounds, validated through simulations.

Findings

Effective modal analysis without full signal reconstruction

Theoretical measurement bounds established for each method

Validated techniques using synthetic and real data simulations

Abstract

Structural Health Monitoring (SHM) systems are critical for monitoring aging infrastructure (such as buildings or bridges) in a cost-effective manner. Such systems typically involve collections of battery-operated wireless sensors that sample vibration data over time. After the data is transmitted to a central node, modal analysis can be used to detect damage in the structure. In this paper, we propose and study three frameworks for Compressive Sensing (CS) in SHM systems; these methods are intended to minimize power consumption by allowing the data to be sampled and/or transmitted more efficiently. At the central node, all of these frameworks involve a very simple technique for estimating the structure's mode shapes without requiring a traditional CS reconstruction of the vibration signals; all that is needed is to compute a simple Singular Value Decomposition. We provide theoretical justification (including measurement bounds) for each of these techniques based on the equations of motion describing a simplified Multiple-Degree-Of-Freedom (MDOF) system, and we support our proposed techniques using simulations based on synthetic and real data.