THESIS
2013
xiv, 147 pages : illustrations ; 30 cm
Abstract
As a promising alternative to wired sensors, wireless sensor networks (WSN) have attracted
widespread attention in the field of structural health monitoring (SHM) due to their unique
features such as lower cost trend, wireless communication and onboard computation. Though
there are many types of modeling and parametric uncertainties in a WSN based SHM system,
the available results are usually restricted to deterministic optimal values while the
uncertainties cannot be quantified. This work is therefore dedicated to the development of
new advanced algorithms for WSN based SHM system with special attention to ambient
modal analysis and structural damage detection using a Bayesian statistical framework.
Firstly, a two-stage fast Bayesian spectral density approach is proposed to ext...[
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As a promising alternative to wired sensors, wireless sensor networks (WSN) have attracted
widespread attention in the field of structural health monitoring (SHM) due to their unique
features such as lower cost trend, wireless communication and onboard computation. Though
there are many types of modeling and parametric uncertainties in a WSN based SHM system,
the available results are usually restricted to deterministic optimal values while the
uncertainties cannot be quantified. This work is therefore dedicated to the development of
new advanced algorithms for WSN based SHM system with special attention to ambient
modal analysis and structural damage detection using a Bayesian statistical framework.
Firstly, a two-stage fast Bayesian spectral density approach is proposed to extract modal
properties and their associated uncertainties for the cases of separated modes and closely
spaced modes, respectively. A novel technique for variable separation is developed so that the
interaction between spectrum variables (e.g., frequency, damping ratio as well as the
amplitude of modal excitation and prediction error) and spatial variables (e.g., mode shape
components) can be decoupled completely. As a result, these two kinds of variables can be
identified separately. The spectrum variables can be identified through ‘fast Bayesian spectral
trace approach’ (FBSTA) in the first stage, while the spatial variables can be estimated in a
second stage by ‘fast Bayesian spectral density approach’ (FBSDA). This study also reveals
the intrinsic relationship between FBSDA and fast Bayesian FFT approach when multiple sets
of measurements are available. The proposed two-stage approach can be implemented in the
environment of WSN through distributed computing strategy so that local mode shape
components confined to different clusters can be identified. A Bayesian mode shape assembly
methodology is herein proposed to form the overall mode shapes so that the weight for
different clusters is accounted for properly according to their data quality. For the proposed
method, there is no need to share the same set of reference dofs for all clusters to obtain
proper scaling.
Next, a novel Bayesian methodology based on the incomplete modal properties (e.g.,
natural frequencies and partial mode shapes of some modes) is developed for structural model
updating. The model updating problem is formulated as one minimizing an objective function, which can incorporate the local mode shape components identified from different clusters
automatically without prior assembling or processing. A fast analytic-iterative scheme is
proposed to efficiently compute the optimal parameters so as to resolve the computational
burden required for optimizing the objective function numerically. The posterior uncertainty
of the model parameters can also be derived analytically and the computational difficulty in
estimating the inverse of the high dimensional Hessian matrix required for specifying the
covariance matrix is also properly treated. The proposed method can avoid the matching
between the measured mode and the model mode, mode shape expansion and eigenvalue
decomposition, which are frequently encountered in conventional model updating approaches.
Finally, the problem of updating a structural model by utilizing non-stationary response
measurements only is considered. A negative log-likelihood function utilized to determine the
posterior most probable parameters and their associated uncertainties is formulated by
incorporating random matrix theory and Bayes’ theorem. Instead of optimizing all the
unknown parameters simultaneously, a numerically iterative coupled method involving the
optimization of the parameters in groups is employed so as to reduce the dimension of the
numerical optimization problem involved. The initial guess for the parameters to be optimized
is also properly estimated. One novel feature of the proposed method is to avoid repeated
time-consuming evaluation of the determinant and inverse of the covariance matrix during
optimization due to exploring the statistical properties of the trace of Wishart matrix.
Moreover, the proposed method allows the monitoring of some critical substructures rather
than the entire structure, requiring no information about the model of the external input or
interface forces.
The efficiency and accuracy of all these methodologies are verified by numerical examples.
Experimental studies are also conducted by employing laboratory shear building models
installed with high-sensitivity accelerometer board (SHM-H sensor board) interfaced to the
advanced wireless sensor node platform (the Crossbow Imote2). The software embedded on
the Crossbow Imote2 is provided by the Illinois Structural Health Monitoring Project (ISHMP)
Services Toolsuite. Successful validation of the proposed methods using measured
acceleration demonstrates the potential for Bayesian approaches to accommodate multiple
uncertainties for WSN based SHM systems.
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