Uncertainty quantification and efficient time-dependent reliability analysis of stochastic dynamic systems

The proposed thesis complements generalized risk assessment frameworks for structural engineering tackling stochastic dynamic systems, by addressing multiple uncertainties, non-linearities, and full-time-dependent analyses. Two major complementary work packages have been pursued. Firstly, a novel point selection procedure for the Probability Density Evolution Method (PDEM) has been developed to enhance efficiency while retaining the full dynamic response of non-linear dynamic systems. This method aims to estimate time-dependent reliability and failure probabilities in dynamic systems under first-passage failure conditions. Leveraging features of the Subset simulation procedure, the Subset supported Point Selection (S-PS) method adaptively generates dependent sample sets, enhancing accuracy by incorporating performance function assessments as weighting factors. The proposed approach effectively identifies samples in the failure region, particularly benefiting dynamic systems under stochastic excitation. It offers a computationally efficient structural reliability estimation procedure by analyzing full-time-history responses, providing deeper insights into rare failure events and mechanisms through visualization of intermediate results. Secondly, to address the challenge of identifying patterns and underlying characteristics in natural or engineering time-varying phenomena, a data-driven stochastic representation of Evolutionary Power Spectral Density (EPSD) functions is introduced. The Relaxed Evolutionary Power Spectral Density (REPSD) function is derived from multiple similar data, accounting for uncertainties and providing a realistic representation of time data such as seismic ground motions or wind speed records in the time-frequency domain. Truncated normal distributions and kernel density estimates are used to determine a probability density function for each time-frequency component. The REPSD function enables the sampling of individual EPSD functions, facilitating their direct application to simulation models through stochastic simulation techniques. Illustrative numerical examples demonstrate the method's effectiveness in accounting for uncertainties in EPSD function estimation and representing the accuracy of time-frequency transformations. Finally, some basic concepts used for the initial formulations of the REPSD were experimentally tested on a self-developed, low-cost, tunable shaking table device called Namazu. The "Shinozuka Benchmark" was introduced, providing a benchmark for testing the accuracy of applied stochastic signals on the table and measuring the responses of the table in the frequency domain. Namazu demonstrated good accuracy and can be adapted to users' needs. The framework has been openly published, and both hardware parts and software are publicly documented.