Executive Summary : | Nonlinear filtering (UKF) is a popular technique for estimating states and parameters of dynamic systems, but it is computationally costly and requires significant tuning for proper convergence. Successful estimation depends on identifying the states/parameters given the measurements, which can result in multiple solutions and invalidate the entire estimation. Identifiability also depends on the model class assumed to describe the system. This research aims to address these issues by developing faster input-state-parameter estimation techniques with robust convergence properties, investigating identifiability of general nonlinear systems in input-state-parameter estimation, and developing techniques to determine model classes that ensure identifiability while realistically describing the system's dynamics. Variants of UKF will be combined with sub-structure identification to improve computational efficiency and applicability to high-dimensional systems. A perturbation approach will be developed to investigate identifiability and determine identifiable sub-sets of inputs/states/parameter given measurements. An equation discovery approach will be developed to determine model classes that fit measurements well with the additional constraint of satisfying identifiability. A damage detection method based on estimated posterior distributions will be developed, with damage extent quantified via damage indices and probability-severity curves. A strategy will be developed to obtain optimal sensor locations for reliable damage detection. The project's outcomes will find direct applications in identification and monitoring of high-dimensional complex dynamic systems in civil infrastructure and mechanical engineering. |