Data Driven Modeling For Analysis And Control Of Dynamical Systems
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Data-Driven Modeling For Analysis And Control Of Dynamical Systems
This dissertation advances the understanding of data-driven modeling and delivers tools to pursue the ambition of complete unsupervised identification of dynamical systems. From measured data only, the proposed framework consists of a series of modules to derive accurate mathematical models for the state prediction of a wide range of linear and nonlinear dynamical systems. Identified models are constructed to be of low complexity and amenable for analysis and control. This developed framework provides a unified mathematical structure for the identification of nonlinear systems based on the Koopman operator. A main contribution of this dissertation is to introduce the concept of time-varying Koopman operator for accurate modeling of dynamical systems in a given domain around a reference trajectory. Subspace identification methods coupled with sparse approximation techniques deliver accurate models both in the continuous and discrete time domains. This allows for perfect reconstruction of several classes of nonlinear dynamical systems, from the chaotic behavior of the Lorenz oscillator to identifying the Newton's law of gravitation. The connection between the Koopman operator and higher-order state transition matrices (STMs) is explicitly discussed. It is shown that subspace methods based on the Koopman operator are able to accurately identify the linear time varying model for the propagation of higher order STMs when polynomial basis are used as lifting functions. Such algorithms are validated on a wide range of nonlinear dynamical systems of varying complexity and are proven to be very effective on nonlinear systems of higher dimension where traditional methods either fail or perform poorly. Applications include model-order reduction in hypersonic aerothermoelasticity and reduced-order dynamics in a high-dimensional finite-element model of the Von Kàrmàn Beam. Numerical simulation results confirm better prediction accuracy by several orders of magnitude using this framework. Additionally, a major objective of this research is to enhance the field of data-driven uncertainty quantification for nonlinear dynamical systems. Uncertainty propagation through nonlinear dynamics is computationally expensive. Conventional approaches focus on finding a reduced order model to alleviate the computational complexity associated with the uncertainty propagation algorithms. This dissertation exploits the fact that the moment propagation equations form a linear time-varying (LTV) system and use system theory to identify this LTV system from data only. By estimating and propagating higher-order moments of an initial probability density function, two new approaches are presented and compared to analytical and quadrature-based methods for estimating the uncertainty associated with a system's states. In all test cases considered in this dissertation, a newly-introduced indirect method using a time-varying subspace identification technique jointly with a quadrature method achieved the best results. This dissertation also extends the Koopman operator theoretic framework for controlled dynamical systems and offers a global overview of bilinear system identification techniques as well as perspectives and advances for bilinear system identification. Nonlinear dynamics with a control action are approximated as a bilinear system in a higher-dimensional space, leading to increased accuracy in the prediction of the system's response. In the same context, a data-driven parameter sensitivity method is developed using bilinear system identification algorithms. Finally, this dissertation investigates new ways to alleviate the effect of noise in the data, leading to new algorithms with data-correlations and rank optimization for optimal subspace identification.
Dynamic Data Driven Applications Systems
This book constitutes the refereed proceedings of the 4th International Conference on Dynamic Data Driven Applications Systems, DDDAS 2022, which took place in Cambridge, MA, USA, during October 6–10, 2022. The 31 regular papers in the main track and 5 regular papers from the Wildfires panel, as well as one workshop paper, were carefully reviewed and selected for inclusion in the book. They were organized in following topical sections: DDAS2022 Main-Track Plenary Presentations; Keynotes; DDDAS2022 Main-Track: Wildfires Panel; Workshop on Climate, Life, Earth, Planets.
Automating Data-Driven Modelling of Dynamical Systems
This book describes a user-friendly, evolutionary algorithms-based framework for estimating data-driven models for a wide class of dynamical systems, including linear and nonlinear ones. The methodology addresses the problem of automating the process of estimating data-driven models from a user’s perspective. By combining elementary building blocks, it learns the dynamic relations governing the system from data, giving model estimates with various trade-offs, e.g. between complexity and accuracy. The evaluation of the method on a set of academic, benchmark and real-word problems is reported in detail. Overall, the book offers a state-of-the-art review on the problem of nonlinear model estimation and automated model selection for dynamical systems, reporting on a significant scientific advance that will pave the way to increasing automation in system identification.