Application of stochastic and machine learning approaches for efficient analysis of dynamical systems

Dynamical systems find a wide range of applications for problems involving response analysis, reliability assessment, and system control of engineering structures, biomechanical structures, and biological models, among others. Especially in civil engineering, structural responses of e.g. buildings, bridges, and offshore structures under time-dependent excitation are determined by dynamic simulations and subsequently the outcomes serve as basis for further performance analyses. Analysis of the system behavior and reliability assessment of dynamically excited systems often requires a considerable number of computationally expensive time-dependent simulations, which is a major challenge, especially for realistic complex models. In order to reduce the computational time and resources model order reduction methods, stochastic approaches e.g. sampling methods and surrogate models as well as supervised machine learning methods e.g. classification and regression approaches have been developed, however it is difficult to generalize the methods and they have to be adapted to the specific problem. In this project, the application of advanced stochastic and machine learning methods for efficient reliability assessment, damage detection, and fatigue evaluation of time-dependent linear and nonlinear dynamic systems is a primary objective. In addition, simplified mechanical models representing the main system behavior and allowing for a fast response evaluation will be calibrated against outcomes of more advanced models or measured data to increase the accuracy of the response analysis and ensure efficient reliability assessment. Therefore the utilized stochastic sampling and surrogate modeling methods as well as machine learning tools are adapted and extended in order to deal with data driven updating for enhanced system analysis.