Uncertainty methods

Basic algorithms

General algorithms are presented for a numerical processing of uncertainty with the characteristics fuzziness, randomness, and fuzzy randomness, which are applicable to a wide range of problems in engineering and beyond.

Fuzzy analysis

Fuzzy analysis is an analysis method for computing system responses with respect to uncertainty of input parameters in a numerically efficient way.

Fuzzy finite element method

Fuzzy finite element method combines the fuzzy analysis with an arbitrary nonlinear finite element algorithm.

Fuzzy stochastic analysis

Fuzzy stochastic analysis involves the mapping of fuzzy random input data onto fuzzy random responses, e.g., displacements and internal forces of structures.

Fuzzy reliability

The fuzzy reliability can be expressed by the fuzzy failure probability.

Fuzzy time series

Analysis and forecast of time series with fuzzy data are introduced by applying fuzzy ARMA processes as well as fuzzy artificial neural networks.

Fuzzy optimization

The extension of crisp optimization methods by considering the uncertainty of structural design parameters is presented. Uncertain structural design parameters are modeled as fuzzy values, which leads to fuzzy objective functions and fuzzy constraints.

Robust structural design

Methods for robust structural design under uncertainty are described.