Uncertainty Quantification in Time Domain Responses with UQLab

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Dear @Eilidh_Radcliff

Welcome to UQWorld!

Let me try to answer your questions in a succinct way:

  1. UQLab is a general-purpose software for uncertainty quantification and propagation, so it can indeed address time-dependent models.
  2. Which UQ method to use is in general dependent on what question you want to solve, and what is the computational cost of a single model run. I suggest you read general hints in this post.
    Monte Carlo simulation usually require many runs of the model, but in the case of your single-degree-of-freedom oscillator, this would not be an issue, so it could be used. The question of surrogate models such as polynomial chaos expansions or Kriging is of interest only to mitigate the computational costs.
  3. No, there are no dedicated module for dynamical systems yet, but bricks exist in different modules. For problems where the dynamics behavior smoothly and slowly changes with the random input parameters, you can use the discretized output trajectories as a vector output and apply any method (including surrogate models construction) directly (UQLab transparently works for models with scalar or vector outputs).
    For problems with rapidly varying outputs, or problems in the frequency domain (frequency response functions), we usually need to do some pre-processing of the trajectory data before constructing surrogate models. You can find details in the following publications:

[1] Mai, C. & Sudret, B., Surrogate models for oscillatory systems using sparse polynomial chaos expansions and stochastic time warping, SIAM/ASA J. Unc. Quant., 2017, 5, 540-571.
[2] Mai, C.-V., Spiridonakos, M. D., Chatzi, E. & Sudret, B., Surrogate modeling for stochastic dynamical systems by combining nonlinear autoregressive with exogeneous input models and polynomial chaos expansions, Int. J. Uncertainty Quantification, 2016, 6, 313-339.
[3] Yaghoubi, V., Marelli, S., Sudret, B. & Abrahamsson, T., Sparse polynomial chaos expansions of frequency response functions using stochastic frequency transformation, Prob. Eng. Mech., 2017, 48, 39-58.

If you have more specific questions on your particular applications, please feel free to ask on this forum.
Best regards
Bruno