Stochastische Finite Elemente Methode (SFEM) an der TU München

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

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

• Sampling methods
• Non-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

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

• Random parameter indetification
• Random parameter discretization
• Model order reduction

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

Mathematical description of inherent random variables

Describing the data

(Ω,F,P)

Ω : sample space

F : event space

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

Time dependent random variable

spatial random variable