This dissertation aims to augment current structural health monitoring (SHM) practice with an approach to model and quantify uncertainty to enable confidence-based decision-making. The SHM application domain is vibration data-based system identification, and more specifically, transmissibility and frequency response function (FRF) estimations are considered, as these are the primary forms of transfer function estimation in the frequency domain. A finite element (FE) model is established in order to supply a benchmark of transmissibility evaluations, and by tuning the FE model, structural damages can be simulated. Two SHM features are proposed to detect and localize defects by analyzing the features calculated at certain interest point arrays. Considering a realistic test condition, all of the model parameters and data are subject to uncertainty from various sources leading to ambiguous system identification results that cause false alarms (Type-I error) when evaluating hypothesis testing for damage. Based upon stationary Gaussian random process, this dissertation statistically establishes uncertainty quantification (UQ) models for different estimators, and uncertainties of transmissibility and FRF are therefore quantified. A perturbation approach is implemented ending up with standard deviation and bias coefficient of transmissibility magnitude estimations. Probability density functions (PDFs) of transmissibility and FRF estimation are derived, for both magnitude and phase, via different methods, namely Chi-square and Gaussian bivariate approach. The proposed statistical models are validated by Monte-Carlo test on both FE simulation model and real lab-scale structure. To obtain a more stringent validation condition, extraneous artificial noise is added onto the raw measurements. Compared to the pre-set confidence interval, validation results are illustrated via outlier percentage, which is the observed outlier amount, at each frequency line, normalized by the number of total test cases. Comparison of the UQ results among different statistical models, estimators, and noise contamination levels is presented, for the purpose of guiding users towards using optimal estimators under certain circumstance. Hypothesis tests are implemented, with statistical models available, and the detection performance is compared for different detectors, damage levels, and noise contaminations. Receiver operating characteristic curves are used for quantitative visualization of the abovementioned performance qualities. Using area under curve (AUC) metric, it is concluded how detection rates trend as damage level and signal-to-noise condition changes, suggesting optimal frequency bands for implementing detection. For example, even for heavily- contaminated cases, there is still acceptable detectability at resonances. As a decision-making problem, SHM probabilistically involves making correct decisions with acceptable (application-dependent) type-I errors. In the end of this dissertation, probability of detection for different cases and test conditions are optimized and compared, as given certain false alarm tolerance thresholds. By having optimal detections, the damage identification problems have a clearer outline with respect to different hypothesis designs

Current control and performance requirements for large- aperture deployable structures call for precise displacement control, with some tolerances approaching micron levels. Given that strain gages are one of the most economically-deployed sensor architectures, we explored two methods for reconstructing displacement from a distributed strain sensing array. One method linearly maps displacement fields to local strains in a supervised learning mode. After loading the system with sufficient cases, a matrix can be established to approach the approximate displacement-strain relationship. The other method is based on linear regression of generalized basis function projections, typically mode shapes. Results of these two approaches are compared for accuracy, robustness, training time, and real-time feasibility. The second method has higher accuracy due to natural modal behaviors, while the first method is feasible if large amount of training cases and measuring points are available

Extracting damage-sensitive features plays an important role in all structural health monitoring applications, as it determines the metrics on which to base decision-making with regard to operation, maintenance, damage state, and so on. This article adopts the widely employed frequency response function, both its magnitude and phase, as the selected feature source and demonstrates how the damage types and locations are able to be classified by means of Bayesian recursive confidence updating. The features are estimated from the in situ acquired vibration data on a rotating machinery test-bed, and the probabilistic models that quantify feature uncertainty are the likelihood functions in a Bayesian framework, which informs the most plausible decisions based on the collected evidence. The damage classification effort in this article specifically calculates the posterior probability, considering the prior and likelihood of data observations; posterior probabilities are then fed back as prior probabilities in the next iteration as new test data are observed. There are three ball-bearing damage conditions applied to the rotary machine test-bed, and the correct model representing the correct damage types will be selected by the model with the maximum posterior confidence. Classification via posterior probability is shown in this article to outperform traditional likelihood evaluations, and the Bayesian recursive implementation distinguishes all three conditions in this work.

System identification in the frequency domain plays a fundamental role in many aspects of mechanical and structural engineering. Frequency domain approaches typically involve estimation of a transfer function, whether it is the usual frequency response function (FRF) or an output-to-output transfer model (transmissibility). The field of structural health monitoring, which involves extracting and classifying features mined from in-sit structural performance data for the purposes of damage condition assessment, has exploited many features for this purpose that inherently are derived from estimations of frequency domain models such as the FRF or transmissibility. Structural health monitoring inevitably involves a hypothesis test at the classification stage such as the (common) binary question: are the features mined from data derived from a reference condition or from data derived from a different (test) condition? Inevitably, this decision involves stochastic data, as any such candidate feature is compromised by error, which we categorize as (i) operational and environmental, (ii) measurement, and (iii) computational/estimation. Regardless of source, this noise leads to the propagation of error, resulting in possible false positive (Type I) errors in the classification. As such, the quantification of uncertainty in the estimation of such features is tantamount to making informed decisions based on a hypothesis test. This paper will demonstrate several statistical models that describe the uncertainty in FRF estimation and will compare their performance to features derived from them for the purposes of detecting damage, with ultimate performance evaluated by receiver operating characteristics (ROCs). A simulation and a plate subject to single-input/single-output vibration testing will serve as the comparison testbeds.

This paper presents a study on localizing damage under stochastic excitation by state-space-based methods, where the damaged response contains some nonlinearity. Two state-space-based modeling algorithms, namely auto- and cross-predictions, are employed in this paper, and the greatest prediction error will be achieved at the sensor pair closest to the actual damage, in terms of localization. To quantify the distinction of prediction error distributions obtained at different sensor locations, the Bhattacharyya distance is adopted as the quantification metric. There are two lab-scale test-beds adopted as validation platforms, including a two-story plane steel frame with bolt loosening damage and a three-story benchmark aluminum frame with a simulated tunable crack. Band-limited Gaussian noise is applied through an electrodynamic shaker to the systems. Testing results indicate that the damage detection capability of the state-space-based method depends on the nonlinearity-induced high frequency responses. Since those high frequency components attenuate quickly in time and space, the results show great capability for damage localization, i.e., the highest deviation of Bhattacharyya distance is coincident with the sensors close to the physical damage location. This work extends the state-space-based damage detection method for localizing damage to a stochastically excited scenario, which provides the advantage of compatibility with ambient excitations. Moreover, results from both experiments indicate that the state-space-based method is only sensitive to nonlinearity-induced damage, thus it can be utilized in parallel with linear classifiers or normalization strategies to insulate the operational and environmental variability, which often affects the system response in a linear fashion. © 2014 IOP Publishing Ltd.

A multivariate time-series analysis employing a state-space embedding strategy and singular value decomposition is presented in this article to detect infrastructure damage. After summarizing the current state-space reconstruction method, the univariate state-space reconstruction is extended to multivariate (or global) reconstruction for observed time series at multiple locations. Under the hypothesis that reconstructed phase state geometry will change with damage, a reduced feature based on Mahalanobis distance of the most significant singular value vector, which is calculated from the reconstructed trajectory, is proposed. Both the area under receiver operating characteristic curve and deflection coefficient are used as comparison metrics to illustrate the presence and severity of damage. The advantage of this proposed approach is computational efficiency and easy implementation using state-space methodology since it does not require high-dimensional neighbor searches, as previous methods have proposed. Validation of the approach is demonstrated using a 6-degree-of-freedom linear spring-mass system and the IASC-ASCE 4-story benchmark experimental structure. Results from both test beds show that damage occurrence and severity can be successfully identified. © The Author(s) 2013.