7.7 Modellierung und Simulation
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The quality of a model - and thus its predictive capabilities - is influenced by numerous uncertainties. They include possibly unknown boundary and initial conditions, noise in the data used for its calibration and uncertainties in the model itself. Here, the latter part is not only restricted to uncertain model parameters, but also refers to the choice of the model itself. Inferring these uncertainties in an automatic way allows for an adaption of the model to new data sets and for a reliable, reproducible model assessment. Note that similar concepts apply at the structural level, where a continuously updated digital twin allows virtual measurements at inaccessible positions of the structure and a simulation based lifetime prediction.
This work presents an inference workflow that describes the difference of measured data and simulated model responses with a generic interface that is independent from the specific model or even the geometry and can easily incorporate multiple data sources. A variational Bayesian inference algorithm is then used to a) calibrate a set of models to given data and to b) identify the best fitting one. The developed concepts are applied to a bridge Demonstrator equipped with displacement sensors, force sensors and a stereophotogrammetry system to perform a system identification of the material parameters as well as a real-time identification of a moving load.
Simulating high-cycle fatigue with continuum models offers the possibility to model stress-redistributions, consider 3Dstress states and simplifies extensions to multi-physics problems. The computational cost of conventional cycle-by-cycle time integrations is reduced by reformulating the fatigue problem as an ordinary differential equation for the material state and solving it with high-order adaptive time integration schemes. The computational cost of calculating the Change of the material state in one cycle is further reduced by a high-order fatigue-specific time integration. The approach is exemplarily demonstrated for a fatigue extension of the implicit gradient-enhanced damage model in 3D and compared to experimental Wöhler lines.
One of the most important goals in civil engineering is to guarantee the safety of the construction. Standards prescribe a required failure probability in the order of 10−4 to 10−6. Generally, it is not possible to compute the failure probability analytically.
Therefore, many approximation methods have been developed to estimate the failure probability. Nevertheless, these methods still require a large number of evaluations of the investigated structure, usually finite element (FE) simulations, making full probabilistic design studies not feasible for relevant applications. The aim of this paper is to increase the efficiency of structural reliability analysis by means of reduced order models. The developed method paves the way for using full probabilistic approaches in industrial applications. In the proposed PGD reliability analysis, the solution of the structural computation is directly obtained from evaluating the PGD solution for a specific parameter set without computing a full FE simulation. Additionally, an adaptive importance sampling scheme is used to minimize the total number of required samples. The accuracy of the failure probability depends on the accuracy of the PGD model (mainly influenced on mesh discretization and mode truncation) as well as the number of samples in the sampling algorithm. Therefore, a general iterative PGD reliability procedure is developed to automatically verify the accuracy of the computed failure probability. It is based on a goal-oriented refinement of the PGD model around the adaptively approximated design point. The methodology is applied and evaluated for 1D and 2D examples. The computational savings compared to the method based on a FE model is shown and the influence of the accuracy of the PGD model on the failure probability is studied.