Uncertainty Quantification in Time Domain Responses with UQLab

Dear UQLab Community,

I am exploring the functionality of UQLab for uncertainty quantification in dynamic systems. Specifically, I am interested in understanding the uncertainty propagation in system responses over time due to variabilities in input parameters.

As a simple example to illustrate my objective, let’s consider a mass-spring-damper system. I am curious to know whether UQLab can handle the UQ for such a system’s response in the time domain, where parameters such as mass (m), damping coefficient (c), and spring constant (k) are uncertain.

Assuming I define probabilistic inputs for the system parameters and integrate a state-space model for the system in UQLab, I am seeking advice on the following:

  1. The possibilities of using UQLab to perform UQ analysis on time-domain responses - for example, through the use of surrogate modeling.
  2. In the context of time-dependent output, which UQ method would be most efficient: Monte Carlo simulations, Polynomial Chaos Expansion, or another approach?
  3. Are there particular modules or functions within UQLab that are tailored for time-domain UQ analysis, or would you recommend a different workflow?
  4. I would be grateful for any shared experiences or insights into similar time-domain UQ analyses, as these could guide my application of UQLab in this context.

Thank you!


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

Dear Bruno,

Thank you for your response.

I’d like to add more context to my initial query. My primary focus is on a 3-degree-of-freedom helicopter model, which includes 12 uncertain inputs. Due to this complexity, Monte Carlo Simulation (MCS) appears to be impractical for my case. The mass-spring-damper system I mentioned earlier was a simplified starting point for my exploration.

Your paper on “Surrogate models for oscillatory systems using sparse polynomial chaos expansions and stochastic time warping” particularly caught my attention. Althoughly I’m currently unsure how to adapt these methodologies to my helicopter model effectively.

I appreciate any guidance or suggestions you might have on how to proceed.

Kind regards,