Identifiability Assessment of Structural Models using an Information-Theoretic Approach
This research aimed at providing an innovative framework for sensor placement to ensure the successful performance of nonlinear structural system identification methods. The accuracy and robustness of a nonlinear structural system and damage identification method highly depends on the amount of information contained in the measured data about the unknown model parameters. It is, therefore, crucial to systematically select the model parameters and to optimally design the type and location of sensors to harvest the maximum information about the model parameters. This was the main goal of this research. This goal is accomplished by investigating the theoretical identifiability conditions of nonlinear structural models using an information-theoretic approach. A statistical metric has been developed to quantify the information contained in every individual measurement channel about every individual model parameter. This one-to-one identifiability measure has been developed by evaluating the difference between the information entropy of the a priori and a posteriori probability distribution function of the model parameters. The proposed identifiability assessment approach can find immediate applications in parameter selection, optimal sensor placement, and design of experiments for general nonlinear models in various engineering disciplines.
Following the initial idea that sparked in my mind, I studied the basics of information theory to be able to tackle this research task. Professor Robert Bitmead, the Cymer Corporation Chair for high-performance dynamic system modeling and control, from UC San Diego Mechanical and Aerospace Engineering Department, has greatly contributed to this research project.