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Uncertainty Quantification

Uncertainty Quantification (UQ) supports the decision-making process by delivering reliable simulation and experimental data with estimated uncertainties due to the impact of imperfectly known information on the design.

Photo: Johan Anderson
Histogram of Monte Carlo (MC) outcome and the outcome distribution from DS method (red curve). Also 95% coverage intervals (MC-dashed lines) and (DS-solid lines), see Olsson, Anderson and Lange 2017.

Uncertainty quantification (UQ) deals with quantitative characterization and limitations of uncertainties in both calculations and experimental evaluations. The basic problem is to determine how credible a result is if certain aspects of the system are not exactly known. When the physical process is controlled by non-linear mechanisms, small variations in the input data can produce a significant change in the result. UQ plays a fundamental role in the quality assurance process and validation of simulation methods and aims to develop rigorous methods to characterize the effects of the model's sensitivity to input, and of the lack of knowledge about these inputs.

Efficient methods

A common approach for sensitivity analysis is a probabilistic approach using repeated simulations where probability distributions are assigned to the parameters to be modelled uncertain. This is most often referred to as Monte Carlo simulations which gives good results but is very costly in terms of simulation time. The main issue being that often only limited set of simulations can be performed within a reasonable time frame. As an alternative to computationally costly random sampling techniques, he application of deterministic sampling (DS) to understand the impact of uncertainties can be used. RISE have successfully implemented DS in several research and customer projects with very positive outcome.

An example, finite element modelling of the stability of a loaded structural beam in a fire resistance test simulated to failure has been analysed using several different approaches to UQ such as VMEA, Fractional Factorial Design, Full Factorial Design, Latin Hypercube Sampling and Polynomial Chaos Expansions. The uncertainties of the input material properties, boundary conditions and loadings propagate through the model and have a large impact on the modelling results as seen below.

Johan Anderson

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