Nowadays, numerical simulations enable the description of mechanical problems in many application fields, e.g. in soil or solid mechanics. During the process of physical and computational modeling, a lot of theoretical model approaches and geometrical approximations are sources of errors and uncertainties. In order to get access to a risk assessment these uncertainties and errors must be captured and quantified. For this aim a new priority program SPP 1886 has been installed by the DFG which focuses on the so called polymorphic uncertainty quantification. In cooperation with the ‘chair of mathematical statistics with applications in biometrics’ we enhance the deterministic structural analysis through two promising approaches of analytical and stochastic sensitivity analysis to capture impacts of the different uncertainties on computational results. Additionally the sensitivities of uncertainties will be compared and rated to develop more efficient methods and tools for the sizing of earth structures in the long-run.
The focus of the project is on quantification and assessment of polymorphic uncertainties in computational simulations for earth structures, especially for fluid-saturated soils. To describe the strongly coupled response behavior, the theory of porous media (tpm) will be used and prepared within the framework of the finite element method (fem) for the numerical solution of initial and boundary value problems. The main objective of the research project is the enhancement of the deterministic structural analysis through two promising approaches of the sensitivity analysis to capture impacts of the different uncertainties on computational results. Additionally the procedures will be compared and rated to develop more efficient methods and tools for the sizing of earth structures in the long-run.
A simple consolidation problem already provided a high sensitivity in the computational results towards variation of material parameters and initial values, see fig.1. The variational and probabilistic sensitivity analyses enable to quantify these sensitivities. The variational sensitivity analysis is a tool for optimization procedures, which captures the impact of different parameters as continuous functions. One advantage is the accurate approximation of the solution space and the efficient computation time, a disadvantage lies in the analytical derivation and algorithmic implementation. Another approach is given by the probabilistic sensitivity analysis from the field of statistics. The expense only increases proportionally to the problems dimension. Instead of a constant value, the model parameters are defined as probability distribution, which provides random values. Thus a set of solution data is built up by several cycles of the simulation. By means of this data base, the probabilistic sensitivity analysis can be applied. Different approaches of the Bayes statistics will enable to receive accurate information with just a few simulations. In detail, the gaussian process regression will be used to create a meta model. By means of the resulting posteriori-distribution the sensitivity analysis will be performed, depending on the choice of the a-priori-distribution. Both approaches will be pursued and advantages and disadvantages will be captured and compared, so that more complex problems can be handled in the long run through further development of the models. Figure 2 shows the objectives of this project chronologically for the first period.