Diagnosis and accuracy enhancement of compressive-sensing signal reconstruction in structural health monitoring using multi-task sparse Bayesian learning

Bayesian compressive sensing (BCS) has provided algorithms to reconstruct underlying signals from far fewer compressed measurements by adopting the theory of sparse Bayesian learning (SBL). However, BCS lacks robustness when the number of measurements is much less than the length of the original signal because signal reconstruction accuracy is sensitive to the specific compressed measurements. As a result, signal reconstruction diagnosis and accuracy enhancement are necessary to tackle this problem. In this study, multi-task SBL is introduced for robust diagnosis and 'healing' of BCS signal reconstruction. A diagnosis technique is proposed to investigate whether the reconstructed (decompressed) signal representation is accurate, based on the phenomenon that inaccurate (suboptimal) signal models are much less stable than accurate (optimal) ones. For accuracy enhancement of compressive sensing signal reconstruction, a modified two-task learning algorithm is developed for potentially improving BCS reconstruction, and the corresponding 'healing' method is presented combined with the diagnosis technique. By applying these methods, the performance of BCS signal reconstruction can be monitored and, when necessary, improved. The real data collected from the structural health monitoring system of a bridge show that the accuracy of BCS reconstruction for automated recovery of data lost during wireless transmission is significantly enhanced by the proposed diagnosis and 'healing' methods.