Bayesian filtering in nonlinear structural systems with application to structural health monitoring

During strong earthquakes structural systems exhibit nonlinear behavior due to low-cycle fatigue, cracking, yielding and/or fracture of constituent elements. After a seismic event it is essential to assess the state of damage of structures and determine if they can safely resist aftershocks or future strong motions. The current practice in post-earthquake damage assessment relies mainly on visual inspections and local testing. These approaches are limited to the ability of inspectors to reach all potentially damaged locations, and are typically intended to detect damage near the outer surfaces of the structure, leaving the possibility of hidden undetected damage. Some structures in seismic prone-regions are instrumented with an array of sensors that measure their acceleration at different locations. Acceleration response measurements contain information about the state of damage of structures, and it is of interest to extract this information and use it in post-earthquake damage assessment and decision making strategies. The objective of this dissertation is to show that Bayesian filters can be successfully employed to estimate the nonlinear dynamic response of instrumented structural systems. The estimated response is subsequently used for structural damage diagnosis in a mechanicsbased framework. Bayesian filters combine dynamic response measurements at limited spatial locations with a nonlinear dynamic model to estimate the response of stochastic dynamical systems at the model degrees-of-freedom. When a subset of the parameters that define the stochastic model are uncertain, these can be estimated together with the response, a strategy known as joint state/parameter estimation. In this dissertation the application of five filters is investigated in the context of structural dynamics applications: the extended, unscented and ensemble Kalman filters, the particle filter and the model-based observer. The main contributions of this dissertation are summarized as follows: i) Development of a filtering-based mechanistic damage assessment framework; ii) Experimental validation of Bayesian filters in small and large-scale structures; iii) Uncertainty quantification and propagation of response and damage estimates; iv) Development of a model-based filter for nonlinear structural systems. Citations Material from this dissertation has been published in the following form: • Hernandez, E. and Erazo, K. (2013). “Experimental verification of a finite element model based functional observer for structural systems”. Proceedings of the 54TH AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. Boston, MA. • Hernandez, E. and Erazo, K. (2013). “Real-Time Dynamic Stress Response Estimation at Critical Locations of Instrumented Structures Embedded in Random Fields”. Proceedings of the 31st IMAC, A Conference on Structural Dynamics. Orlando, FL. • Erazo, K. and Hernandez, E. (2013). “Nonlinear Model-Data Fusion for PostEarthquake Assessment of Structures”. Proceedings of the 9th International Workshop on Structural Heath Monitoring. Stanford University, Stanford, CA. • Erazo, K. and Hernandez, E. (2014). “A model-based observer for state and stress estimation in structural and mechanical systems: Experimental validation”. Mechanical Systems and Signal Processing, 43:141-152. • Erazo, K. and Hernandez, E. (2014). “Real-time efficient state estimation in nonlinear structural systems”. Proceedings of the 9th International Conference on Structural Dynamics, EURODYN. Porto, Portugal. • Erazo, K. and Hernandez, E. (2014). “Uncertainty quantification for state estimation in nonlinear structural systems”. Proceedings of the Second International Conference on Vulnerability and Risk Analysis and Management (ICVRAM) and the Sixth International Symposium on Uncertainty, Modeling, and Analysis (ISUMA). Liverpool, United Kingdom. • Erazo, K. and Hernandez, E. (2014). “State Estimation in Nonlinear Structural Systems”. Proceedings of the 32nd IMAC, A Conference on Structural Dynamics. Orlando, FL. And Material from this dissertation has been submitted for publication to the ASCE Journal of Engineering Mechanics on August 2014 in the following form: • Erazo, K. and Hernandez, E. “A mechanistic approach to post-earthquake damage assessment of instrumented structures with uncertain input”.