Subspace system identification of support excited structures—part II: gray-box interpretations and damage detection

A theoretical framework is presented for the estimation of the physical parameters of a structure (i.e., mass, stiffness, and damping) from measured experimental data (i.e., input–output or output-only data). The framework considers two state-space models: a physics-based model derived from first principles (i.e., white-box model) and a data-driven mathematical model derived by subspace system identification (i.e., black-box model). Observability canonical form conversion is introduced as a powerful means to convert the data-driven mathematical model into a physically interpretable model that is termed a gray-box model. Through an explicit linking of the white-box and gray-box model forms, the physical parameters of the structural system can be extracted from the gray-box model in the form of a finite element discretization. Prior to experimental verification, the framework is numerically verified for a multi-DOF shear building structure. Without a priori knowledge of the structure, mass, stiffness, and damping properties are accurately estimated. Then, experimental verification of the framework is conducted using a six-story steel frame structure under support excitation. With a priori knowledge of the lumped mass matrix, the spatial distribution of structural stiffness and damping is estimated. With an accurate estimation of the physical parameters of the structure, the gray-box model is shown to be capable of providing the basis for damage detection. With the use of the experimental structure, the gray-box model is used to reliably estimate changes in structural stiffness attributed to intentional damage introduced. Copyright © 2012 John Wiley & Sons, Ltd.