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...[ Read more ]

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.