A probability density functional framework for the probabilistic response and reliability analysis of dynamical structural systems subjected to random environmental loads

• Applicant: Zifeng Huang, Ph.D.
• Subject Area: Applied Mechanics, Statics and Dynamics
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 554325683

In the pursuit of a safe and economical design for diverse real infrastructures, accurately predicting structural dynamic responses caused by random environmental loads is a significant and challenging issue. One key research objective in this field is to obtain a comprehensive probabilistic description of structural dynamic responses, allowing for the determination of any statistical and probabilistic properties of the structural behavior. However, current state-of-the-art analysis techniques, which typically consider only a few statistical moments or an evolutionary probability density function (PDF) of structural responses, fall short of achieving this objective. The objective of this project is to develop a novel probability density functional (PDFL) framework for calculating the joint PDF of structural dynamic responses at multiple time instants and the dynamic response first-passage probability due to non-Gaussian and non-stationary random excitation processes. First, random loads will be modeled using the mixed Gaussian PDFL. A path integral methodology for the joint PDF of structural responses at multiple time instants will be developed by applying the load PDFL model to the dynamic structure differential equation. Subsequently, by approximating a functional integral as a finite-dimensional probabilistic integral using the Karhunen-Loève (KL) expansion and computing the probabilistic integral with the importance sampling method, a novel direct PDFL integral method to calculate structural dynamic and extreme response probability distributions will be developed. Finally, with a newly proposed deterministic control determination method, an efficient importance sampling approach will be developed to estimate the response first-passage probability of dynamic structural systems driven by general random loads. This proposed framework is versatile, accounting for diverse structural systems with sophisticated nonlinearities, e.g., complex hysteresis and fractional derivatives. It is applicable to the probability and reliability analysis of real high-dimensional structures subjected to random environmental loads. The findings from this envisaged project will lead to a more profound insight into the uncertainty propagation from random loads to structural dynamic responses. The proposed PDFL framework can enhance the precision of dynamic response predictions for critical infrastructures, such as super-tall buildings and long-span bridges, exposed to random environmental loads. These advancements will promote more comprehensive analyses and the creation of safer and economic designs of engineering structures, ultimately contributing to solving one of the global challenges and a sustainable development goal of the UN - resilient urban infrastructure.

• DFG Programme: Research Grants
• International Connection: Australia, USA
• Cooperation Partners: Professor Ioannis Kougioumtzoglou, Ph.D.; Professor Athanasios Pantelous, Ph.D.