This project will improve the treatment of uncertainty in the process of model identification. It is often useful to mathematically represent both the external influences acting on a real system, and the response of the system to those inputs. The system itself can then be modeled as a mathematical object that converts inputs into responses. Model identification is the process of determining the form of the model -- and of assigning values to any parameters that it may require -- based on observation of the inputs and outputs. Systems that are subject to random variations are called stochastic. When inputs are applied to a stochastic system, it can be difficult to distinguish between the repeatable part of the response and the part of the response due to random fluctuations. This difficulty inevitably causes uncertainty in the resulting system model. The results of this project will enable these uncertainties to be handled as well as possible in several important cases that cannot currently be treated. These are systems that change over time, systems with missing input/response data, and systems with certain types of complex dynamic behavior. The importance of such approaches is paramount for further development of system damage/fault detection procedures. Such diagnostic methods can be integrated in a broader framework for real-time monitoring of the dynamic behavior of the system as well as assessing its reliability. The project will contribute to diverse research fields such as structural dynamics, probabilistic methods, data acquisition and signal processing, as well as structural safety and reliability. For instance, to restore and improve urban infrastructure, uncertainties related to ageing mechanisms and environmental excitations need to be identified and quantified. In addition, e-learning interactive software tools will be deployed online, incorporating research results from this project.
This project will advance knowledge in the fields of uncertainty modeling and quantification, with emphasis on stochastic excitation modeling and structural system identification subject to highly limited data. Specific challenges related to modeling of the uncertainties, and the identification of the structural system properties based on knowledge of input-output (excitation-response) data include: (1) measured/available data most often possess evolutionary features, i.e. they exhibit a time-varying behavior, (2) most often there are limited, incomplete and/or missing data, and (3) the system governing equations are highly complex from a mathematics perspective, including nonlinearities and fractional derivatives modeling. Currently, it is not possible to address cases (1), (2), and (3) simultaneously in a consistent, efficient manner. The research objective of this project is to create a compressive sampling based methodology for efficient uncertainty modeling and quantification in the field of stochastic engineering dynamics subject to highly limited data. Specific goals include the development of techniques for spectral analysis and stochastic process statistics estimation subject to incomplete data, as well as for identifying the parameters of nonlinear systems endowed with fractional derivative elements. Preliminary work suggests satisfactory accuracy for up to 80% missing data.
