Efficient Computational Methods for Stochastic Analysis of Large-Scale Structural Dynamic Systems

Quickly determining the dynamic response of complex structures, such as buildings and bridges, when faced with uncertainties that can include, but are not limited to, actual member dimensions and loads they experience, is still a challenge for today's advanced computer modeling tools. Research funded by this award aims to create new methods for analyzing the behavior of complex engineering systems and structures in the presence of uncertainty, advancing scientific progress and improving civil infrastructure safety.

Advances in experimental techniques and emerging technologies have led to increasingly complex mathematical models for large-scale systems. Current methods for solving these models exhibit either high accuracy or computational efficiency, but not both. This restriction limits the effectiveness of the methods for system analysis, design and optimization.

This research will create a novel solution methodology that combines high accuracy with computational efficiency, enabling more reliable and efficient analysis of structural systems. The methodology will also impact emerging technologies like the use digital representations of actual structures, where accurate predictions of a system's future performance are critical for informed decision-making.

Advancements from this research will enhance infrastructure resilience and support emerging industries. Additionally, the project includes innovative education, outreach, and community engagement activities to inspire the next generation of researchers, engineers and educators, helping create a diverse and skilled STEM workforce.

The research objective of this project is to create a methodology for efficiently and accurately addressing uncertainty propagation in structural dynamics problems. The approach aims to revolutionize the field of stochastic structural dynamics by achieving drastic improvements (spanning several orders of magnitude) in computational efficiency. Central to this effort is the creation of a joint time-space extrapolation methodology for determining the non-stationary response joint probability density function (PDF) of high-dimensional structural systems.

Unlike existing methods, which become computationally prohibitive for high-dimensional systems due to the exponential growth of computational cost with the number of degrees of freedom, this methodology intends to overcome the curse of dimensionality by striving to leverage information embedded in the time-history of the most probable Wiener path integral path. It also intends to introduce a variational formulation of the problem with mixed fixed/free boundary conditions that renders computational cost independent of the total number of degrees of freedom.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.