Signal compression is often important to reduce the cost of data transfer and storage
for structural health monitoring (SHM) systems of civil structures. 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. In this article, we study 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 sub-optimal 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. The
numerical results also are given to validate the proposed method.