A proper general decomposition approach for an efficient structural reliability analysis

• Applicants: Dr.-Ing. Annika Robens-Radermacher; Dr.-Ing. Jörg F. Unger
• Subject Area: Applied Mechanics, Statics and Dynamics
• Term: since 2017
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 326557591

All engineering disciplines aim at robust products and structures. Therefore, the assessment of the reliability of such products and structures is important over their whole life time: development, construction, operation and decommission. The goal of reliability analysis is the computation of the probability of failure. Especially in case of structural reliability analysis, very small failure probabilities are expected, because structural failure is very rare. In the literature, a variety of approaches for estimating the probability of failure can be found. These calculations generally involve a complex nonlinear finite element simulation, which leads to a computationally expensive analysis. Recent methods aim to decrease the number of required deterministic calculations, to reduce the high computational effort. Nevertheless, such approaches still require a few thousand calculations of the underlying finite element model. The idea of the proposal is to use model reduction techniques to improve the computational efficiency of the reliability analysis. Model reduction is a popular concept to decrease the computational effort of complex numerical simulations. The concept is recently used in a variety of applications. The aim of the proposal is to develop a model order approach which can be used for the underlying computationally intensive finite element simulations of a reliability analysis. The combined reliability method with model reduction leads to an efficient computation of the probability of failure. For this purpose, the proper general decomposition (PGD) method is developed for nonlinear structural problems with random parameters as additional coordinates. The displacements as well as the internal variables, in case of nonlinearity, are approximated by a separated form including the random parameters resulting from the reliability analysis. The approach leads to solution of a complex finite element simulation in a separated form for the whole parameter space. The reduced model is adaptively coupled within the reliability analysis. Therefore, the reliability problem is decomposed in several sub-problems with higher failure probabilities. The probability of failure is estimated as product of the conditional failure probabilities. The conditional probabilities are computed based on PGD simulations generated for each sub-problem. By means of the solution of the reduced model, each limit state function can be derived in a separated form. This function can be evaluated with low computational effort. Consequently, each conditional probability can be estimated in a very efficient way. The developed method can be generally applied to all kinds of structural reliability problems. In the proposal, the efficiency of the method is validated by investigating the influence of creep on the reliability of a prestressed reinforced concrete structure.

• DFG Programme: Research Grants