Robust Diagnostics for Bayesian Compressive Sensing with Applications to Structural Health Monitoring

In structural health monitoring (SHM) systems for civil structures, signal compression is often important to reduce the cost of data transfer and storage because of the large volumes of data generated from the monitoring system. Compressive sensing is a novel data compressing method whereby one does not measure the entire signal directly but rather a set of related ("projected") measurements. The length of the required compressive-sensing measurements is typically much smaller than the original signal, therefore increasing the efficiency of data transfer and storage. Recently, a Bayesian formalism has also been employed for optimal compressive sensing, which adopts the ideas in the relevance vector machine (RVM) as a decompression tool, such as the automatic relevance determination prior (ARD). Recently publications illustrate the benefits of using the Bayesian compressive sensing (BCS) method. However, none of these publications have investigated the robustness of the BCS method. We show that the usual RVM optimization algorithm lacks robustness when the number of measurements is a lot less than the length of the signals because it can produce suboptimal signal representations; as a result, BCS is not robust when high compression efficiency is required. This induces a tradeoff between efficiently compressing data and accurately decompressing it. Based on a study of the robustness of the BCS method, diagnostic tools are proposed to investigate whether the compressed representation of the signal is optimal. With reliable diagnostics, the performance of the BCS method can be monitored effectively. The numerical results show that it is a powerful tool to examine the correctness of reconstruction results without knowing the original signal.