A Subdomain Approach for Uncertainty Quantification of Long Time Horizon Random Processes 2023-01-0083

This paper addresses the uncertainty quantification of time-dependent problems excited by random processes represented by Karhunen Loeve (KL) expansion. The latter expresses a random process as a series of terms involving the dominant eigenvalues and eigenfunctions of the process covariance matrix weighted by samples of uncorrelated standard normal random variables. For many engineering appli bn vb nmcations, such as random vibrations, durability or fatigue, a long-time horizon is required for meaningful results. In this case however, a large number of KL terms is needed resulting in a very high computational effort for uncertainty propagation. This paper presents a new approach to generate time trajectories (sample functions) of a random process using KL expansion, if the time horizon (duration) is much larger than the process correlation length. Because the numerical cost of KL expansion increases drastically with the size of time horizon, we partition it into multiple subdomains of equal length (time), perform a KL expansion for only the first subdomain and then extend it to the remaining subdomains by imposing a correlation between the KLE coefficients of adjacent subdomains. Additionally, to ensure continuity at the junction between subdomains, a cubic spline interpolation is implemented. The proposed approach is demonstrated using two examples.