An enhanced method to reduce reconstruction error of compressed sensing for structure vibration signals

Abstract

Compressed sensing (CS) utilizes the signal’s sparsity to reconstruct signals from far less linear measurements. However, ambient vibration response in structural dynamics typically lacks sparsity on a regular transform basis. Hence, when the vibration signals are reconstructed through the CS, significant errors are unavoidably induced, especially at high compression ratios, limiting the CS applicability in structural health monitoring and damage detection. To address these issues, this paper proposes an enhanced error reduction method, exploited as a post-processing scheme for signal reconstruction. The suggested method constructs an autoregression model, whose residuum increases to correspond to the reconstruction error based on empirical observations. Through minimizing the residuum under the constraint of compressed measurements, the reconstruction error is then minimized, which leads to an optimized result of the reconstructed signals. The suggested method is validated using ambient vibration data collected from a laboratory-scale shear frame model and a full-scale cable-stayed bridge.