Katana VentraIP

Uncertainty quantification

Uncertainty quantification (UQ) is the science of quantitative characterization and estimation of uncertainties in both computational and real world applications. It tries to determine how likely certain outcomes are if some aspects of the system are not exactly known. An example would be to predict the acceleration of a human body in a head-on crash with another car: even if the speed was exactly known, small differences in the manufacturing of individual cars, how tightly every bolt has been tightened, etc., will lead to different results that can only be predicted in a statistical sense.

Many problems in the natural sciences and engineering are also rife with sources of uncertainty. Computer experiments on computer simulations are the most common approach to study problems in uncertainty quantification.[1][2][3][4]

To evaluate low-order moments of the outputs, i.e. and variance.

mean

To evaluate the reliability of the outputs. This is especially useful in where outputs of a system are usually closely related to the performance of the system.

reliability engineering

To assess the complete probability distribution of the outputs. This is useful in the scenario of optimization where the complete distribution is used to calculate the utility.

utility

Simulation-based methods: , importance sampling, adaptive sampling, etc.

Monte Carlo simulations

General surrogate-based methods: In a non-instrusive approach, a is learnt in order to replace the experiment or the simulation with a cheap and fast approximation. Surrogate-based methods can also be employed in a fully Bayesian fashion. [10][4][11][12] This approach has proven particularly powerful when the cost of sampling, e.g. computationally expensive simulations, is prohibitively high.

surrogate model

Local expansion-based methods: , perturbation method, etc. These methods have advantages when dealing with relatively small input variability and outputs that don't express high nonlinearity. These linear or linearized methods are detailed in the article Uncertainty propagation.

Taylor series

Functional expansion-based methods: Neumann expansion, orthogonal or Karhunen–Loeve expansions (KLE), with and wavelet expansions as special cases.

polynomial chaos expansion (PCE)

Most probable point (MPP)-based methods: first-order reliability method (FORM) and second-order reliability method (SORM).

Numerical integration-based methods: Full factorial numerical integration (FFNI) and dimension reduction (DR).

Computer experiment

Further research is needed

Quantification of margins and uncertainties

Probabilistic numerics

Bayesian regression

Bayesian probability