Weighting Matrices and Model Order Determination in Stochastic System Identification for Civil Infrastructure Systems

This research work consists in the development of a new robust stochastic system identification technique for the identification of dynamic characteristics of large-scale and complex civil infrastructure systems. Based on a stochastic state-space model framework, a new approach for state variable estimation is developed by proposing a new set of weighting matrices for the purpose of properly determining the order of a numerical model of the structure under consideration. For the development of such a new approach, a theoretical interpretation and investigation of the stochastic system identification process is provided within a general framework of the stochastic subspace method.;This work addresses four main topics of research: (1) to define existing stochastic subspace approaches in a unified framework that can be readily modified according to a desired performance. This unification is performed in a general multivariate analysis framework by using certain sets of weighting matrices; (2) to evaluate differences of the existing approaches in their performances for system identification. In this phase of research, after the investigation of the properties that each approach considers in its identification process of a dynamic system, the evaluation of their performance is conducted, in numerical and practical applications, with respect to the ability to highlight structural properties against noise ones in terms of the solution for singular value problem; (3) to develop a new robust stochastic subspace approach that properly discriminates structural modes, including both strongly and weakly excited modes, from noise ones in estimating state vectors from the singular value problem. Such a new approach is developed by proposing a new set of weighting matrices and its efficiency over the existing approaches is verified by using analytical, experimental and field data; and (4) to address frequently encountered problems in practical applications of a general subspace method. Considering such problems, complementary methods for the implementation of the subspace method are also investigated.