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.

Guided wave (GW) testing has become one of the most important nondestructive tools for evaluation of structural in-service degradation. Although GW testing was widely used to inspect and screen many engineering structures, there are still challenges associated with its applications, which mostly originate from the dispersive and multi-mode nature of GW signals as well as noise contamination. To deal with these challenges, an effective GW signal processing technique is introduced that enables one to accurately recover multiple modes from noisy dispersive GW signals for defect localization. To characterize the dispersion phenomenon, the chirp model is introduced first, which is derived from GW dispersion characteristics. Based on this model, an over-complete dictionary is designed by considering all possible defect locations (by discretization) and the propagation paths of GW modes caused by these defects. Then the prior knowledge that structural defects or damage typically occur in localized areas and correspondingly only a small number of modes are included in the GW signals is exploited by a robust sparse Bayesian learning (SBL) framework to reduce the ill-conditioning in the inverse problem. During the implementation of the robust SBL algorithm, irrelevant basis vectors in the dictionary are pruned out and the posterior probabilities of the small number nonzero basis coefficients corresponding to those “active” GW modes are established. After sparse representation of the GW signal, the information of propagation paths and group delays of GW modes are used to identify each GW mode and then localize defects. Illustrative results from numerical simulations and experiment studies on plate structures are presented to demonstrate the capability of the proposed method.

Ultrasonic nondestructive testing (NDT) provides a valuable insight into the integrity of stainless steel structures, but the noise caused by the scattering of stainless steel microstructure often limits the effectiveness of inspection. This work presents a novel adaptive filtering approach to enhance the signal-to-noise ratio (SNR) of a measured ultrasonic signal from the inspection of a stainless steel component, enabling the detection of hidden flaws under strong noise. After the spectral modeling of the noisy ultrasonic NDT signal, the difference between the spectral characteristics of a flaw echo and that of grain noise is highlighted, and a reference spectrum model to estimate the frequency spectrum of the echo reflected by any possible flaw is developed. Then, the signal is segmented and the similarity between the spectra of data segments and the reference spectra is evaluated quantitatively by the spectral similarity index (SSI). Based on this index, an adaptive time-frequency filtering scheme is proposed. Each data segment is processed by the filtering to suppress the energy of noise. The processed data segments are recombined to generate the de-noised signal after multiplying weighting coefficients, which again is determined by the SSI. The performance of the proposed method for SNR enhancement is evaluated by both the simulated and experimental signal and the effectiveness has been successfully demonstrated.

Ultrasonic sensors have been extensively used in the nondestructive testing of materials for flaw detection. For polycrystalline materials, however, due to the scattering nature of the material, which results in strong grain noise and attenuation of the ultrasonic signal, accurate detection of flaws is particularly difficult. In this paper, a novel flaw-detection method using a simple ultrasonic sensor is proposed by exploiting time-frequency features of an ultrasonic signal. Since grain scattering mostly happens in the Rayleigh scattering region, it is possible to separate grain-scattered noise from flaw echoes in the frequency domain employing their spectral difference. We start with the spectral modeling of grain noise and flaw echo, and how the two spectra evolve with time is established. Then, a time-adaptive spectrum model for flaw echo is proposed, which serves as a template for the flaw-detection procedure. Next, a specially designed similarity measure is proposed, based on which the similarity between the template spectrum and the spectrum of the signal at each time point is evaluated sequentially, producing a series of matching coefficients termed moving window spectrum similarity (MWSS). The time-delay information of flaws is directly indicated by the peaks of MWSSs. Finally, the performance of the proposed method is validated by both simulated and experimental signals, showing satisfactory accuracy and efficiency.