Compared with the conventional monitoring approach of separately sensing and then compressing the data, compressive
sensing (CS) is a novel data acquisition framework whereby the compression is done during the sampling. If the original
sensed signal would have been sufficiently sparse in terms of some orthogonal basis, the decompression can be done
essentially perfectly up to some critical compression ratio. In structural health monitoring (SHM) systems for civil
structures, novel data compression techniques such as CS are needed to reduce the cost of signal transfer and storage. In
this article, Bayesian compressive sensing (BCS) is investigated for SHM signals. By explicitly quantifying the
uncertainty in the signal reconstruction, the BCS technique exhibits an obvious benefit over the existing regularized
norm-minimization CS. However, current BCS algorithms suffer from a robustness problem; sometimes the
reconstruction errors are large. The source of the problem is that inversion of the compressed signal is a severely ill-posed
problem that often leads to sub-optimal signal representations. To ensure the strong robustness of the signal
reconstruction, even at a high compression ratio, an improved BCS algorithm is proposed which uses stochastic
optimization for the automatic relevance determination approach to reconstructing the underlying signal. Numerical
experiments are used as examples; the improved BCS algorithm demonstrates superior performance than state-of-the-art
BCS reconstruction algorithms.
Earthquake early warning (EEW) systems are currently operating nationwide in Japan and are in beta-testing
in California. Such a system detects an earthquake initiation using online signals from a seismic sensor
network and broadcasts a warning of the predicted location and magnitude a few seconds to a minute or so
before an earthquake hits a site. Such a system can be used synergistically with installed structural health
monitoring (SHM) systems to enhance pre-event prognosis and post-event diagnosis of structural health. For
pre-event prognosis, the EEW system information can be used to make probabilistic predictions of the
anticipated damage to a structure using seismic loss estimation methodologies from performance-based
earthquake engineering. These predictions can support decision-making regarding the activation of
appropriate mitigation systems, such as stopping traffic from entering a bridge that has a predicted high
probability of damage. Since the time between warning and arrival of the strong shaking is very short,
probabilistic predictions must be rapidly calculated and the decision making automated for the mitigation
actions. For post-event diagnosis, the SHM sensor data can be used in Bayesian updating of the probabilistic
damage predictions with the EEW predictions as a prior. Appropriate Bayesian methods for SHM have been
published. In this paper, we use pre-trained surrogate models (or emulators) based on machine learning
methods to make fast damage and loss predictions that are then used in a cost-benefit decision framework for
activation of a mitigation measure. A simple illustrative example of an infrastructure application is presented.
KEYWORDS: Diagnostics, Compressed sensing, Structural health monitoring, Data storage, Signal processing, Signal detection, Data compression, Interference (communication), Optimization (mathematics), Sensor networks
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 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. 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.
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