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Stochastische Finite Elemente Methode (SFEM)

Methods to model epistemic uncertainty

- Fuzzy method
- Interval analysis
- Sensitivity derivatives
- Evidence theory
- Convex modeling

Stochastische Finite Elemente Methode (SFEM)

Methods to model aleatoric uncertainty

- Monte Carlo (MC) simulation
- Reliability based methods (FORM, SORM)
- Pertubation method
- Response surface method
- Spectral method

Stochastische Finite Elemente Methode (SFEM)

Types of Probabilistic methods

- Sampling methods
- Non-sampling methods

Stochastische Finite Elemente Methode (SFEM)

Pros and cons of sampling methods

Pros:

- simple, straight fordward to apply
- no complicated math needed
- FEM model can be used as black box

Cons:

- inefficient and time-consuming for large scale problems
- large range of uncert. requires large number of parameter realizations

Stochastische Finite Elemente Methode (SFEM)

Pros and cons of nonsampling methods

Pros:

- parameters are approximated by analytical and unique functions
- only few model realizations required
- FEM model as black box
- more efficient than sampling methods

Cons:

- abstract mathmatics needed
- not straightforward for dependent uncertainty parameters

Stochastische Finite Elemente Methode (SFEM)

Challenges in SFEM

- Random parameter indetification
- Random parameter discretization
- Model order reduction

Stochastische Finite Elemente Methode (SFEM)

What is the difference between a deterministic and stochastic system?

- deterministic: for known inputs outcome ispredictable
- stochastic: outcome not fully predictable

Stochastische Finite Elemente Methode (SFEM)

What is probability theory?

Mathematical description of inherent random variables

Stochastische Finite Elemente Methode (SFEM)

What is statistics?

Describing the data

Stochastische Finite Elemente Methode (SFEM)

What does a Probability space consist of?

(Ω,F,P)

Ω : sample space

F : event space

P : probability measure (assigns a probability to an event in F)

Stochastische Finite Elemente Methode (SFEM)

What is a random process?

Time dependent random variable

Stochastische Finite Elemente Methode (SFEM)

What is a random field?

spatial random variable

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