A time variant uncertainty propagation method for high-dimensional dynamic structural system via K-L expansion and...

Area of Science:

• Structural Engineering
• Computational Mechanics
• Applied Mathematics

Background:

• Dynamic structural systems often involve high-dimensional input variables with time-varying uncertainties.
• Accurate uncertainty propagation is crucial for reliable structural design and risk assessment.
• Existing methods struggle with the complexity of high-dimensional, non-stationary stochastic processes.

Purpose of the Study:

• To propose a novel time variant uncertainty propagation (TUP) method for dynamic structural systems with high-dimensional inputs.
• To develop an arbitrary stochastic process simulation (ASPS) method suitable for non-stationary processes.
• To integrate ASPS with Bayesian deep neural networks for efficient uncertainty quantification.

Main Methods:

• Developed an arbitrary stochastic process simulation (ASPS) using Karhunen-Loève (K-L) expansion and numerical integration.
• Employed an iterative sorting method to match statistical samples with covariance function constraints.
• Converted high-dimensional TUP problems into static uncertainty propagation (UP) problems, solved using Bayesian deep neural networks.

Main Results:

• The proposed ASPS method effectively represents stochastic processes using marginal distributions and eigenfunctions.
• The integration of ASPS and Bayesian deep neural networks successfully solves high-dimensional TUP problems.
• Numerical examples validated the effectiveness and accuracy of the developed TUP method.

Conclusions:

• The proposed TUP method provides an efficient and accurate approach for analyzing dynamic structural systems with complex uncertainties.
• The method is suitable for both stationary and non-stationary stochastic processes with arbitrary marginal distributions.
• This work contributes to physics-informed machine learning applications in structural integrity.