Bayesian inference provides a powerful approach to system identification and damage assessment for structures. The application of Bayesian method is motivated by the fact that inverse problems in structural engineering, including structural health monitoring, are typically ill-conditioned and ill-posed when using noisy incomplete data because of various sources of modeling uncertainties. One should not just search for a single ''optimal'' value for the vector of model parameters but rather attempt to describe the whole family of plausible model parameters based on measured data using a Bayesian probabilistic framework. In this article, the fundamental principles of Bayesian analysis and computation are summarized; then a review is given of recent state-of-the-art practices of Bayesian inference in system identification and damage assessment for civil infrastructure. Discussions of the benefits and deficiencies of these approaches, as well as potentially useful avenues for future studies, are also provided. Our focus is on meeting challenges that arise from system identification and damage assessment for the civil infrastructure but our presented theories also have a considerably broader applicability for inverse problems in science and technology.

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.

In this paper, a new fractal theory-based acoustic emission (AE) signal processing method is proposed. It is found that both the curve lengths and fractal dimensions (FDs) of AE signal are related with damage evolution. The AE tests of pseudo-static experiment of a reinforced concrete column (RCC), a reinforced nano-concrete column and a concrete-filled glass fibre reinforced polymer (GFRP) tube are then performed for validation. For each specimen, several piezoelectric ceramic (PZT) patches and one AE sensor are bonded at different positions of the specimen surface to monitor the AE signals.The results show that the fractal theory-based damage method can assess damage evolution effectively. In addition, the damage can be localised approximately by the diversity of damage assessing index values from various PZT detectors.

In this paper, a new fractal theory-based acoustic emission (AE) signal processing method is proposed. It is found that both the curve lengths and fractal dimensions (FDs) of AE signal are related with damage evolution. The AE tests of pseudo-static experiment of a reinforced concrete column (RCC), a reinforced nano-concrete column and a concrete-filled glass fibre reinforced polymer (GFRP) tube are then performed for validation. For each specimen, several piezoelectric ceramic (PZT) patches and one AE sensor are bonded at different positions of the specimen surface to monitor the AE signals.The results show that the fractal theory-based damage method can assess damage evolution effectively. In addition, the damage can be localised approximately by the diversity of damage assessing index values from various PZT detectors.