Stochastic optimization of structural health monitoring techniques -

Abstract

The modeling of complex nonlinear structures is always accompanied with different sources of uncertainties. These uncertainties become significant when the structural system is subjected to regular aging factors or to some extreme events that could alter its behavior unexpectedly. Thus to reduce failure risks, and improve the knowledge of the system state and parameters, Structural Health Monitoring (SHM) techniques are employed for early detecting the damage of such structural systems. This process relies on analyzing collected real time measurements using Data Assimilation techniques. The Kalman Filter (KF) method and its different variations fall in the class of Sequential Data Assimilation techniques; these techniques start by calibrating the model parameters and then update them in response to any change in the material’s behavior, based on an optimal probabilistic framework that minimizes the mismatch between the predicted values and actual measurements. In this dissertation, a highlight on the importance of uncertainty quantification is presented through a comparative study between intrusive and non-intrusive ways in quantifying uncertainties. A comparison between two different variations of the Kalman filter technique, the Ensemble Kalman Filter (EnKF) and the Polynomial Chaos based Ensemble Kalman Filter (PCKF), is performed for this purpose. The comparison is based on the ability and efficiency of each technique in quantifying the present uncertainties and in properly identifying the state and parameters of the system under consideration. A four-degrees of freedom (DOFs) system subjected to El-Centro earthquake ground excitation is used to compare the EnKF to the PCKF in representing the uncertainties for SHM purposes. A preset damage of the first degree-of-freedom of the system is imposed. The Bouc-Wen model is used for the forecast and analysis steps of both KF variations as well as for synthetically generating the measurements of displacements and velocities at each DOF for parametric calibra