Coupling engineering simulations with stochastic analysis for uncertainty quantification and parameter identification
The dynamically growing field of uncertainty quantification and Bayesian identification is just beginning to enter into engineering practice. Stochastic analysis is not only used for simulating true randomness, but our lack of knowledge of material properties, modelingerrors or model coefficients can also be modeled as random variables, random fields or random processes with a Bayesian approach.
The analysis of the changing of properties and quality of buildings and infrastructures within the GRK 2075 program is typically done by highly sophisticated nonlinear, multi-scale models. Most of these models however are very sensitive to their input parameters or model coefficients, which are usually only known with limited precision. The coupling of probabilistic analysis with the governing equations enables the analysis of the propagation of these uncertainties through the model response. This approach provides not only methods to quantify uncertainties and global sensitivities, but also bases a robust validation and parameter identification method in the framework of Bayesian inversion.
The most popular methods among engineers to analyze the propagation of uncertainties are the brute force Monte Carlo (MC) type of sampling based methods. These methods necessitate an excessive computational burden, because a large number of executions of the deterministic simulation is needed for accurate statistical information. However, its simplicity and the decoupled, non-intrusive manner to calculate the impact of uncertainties still seem to make these methods an attractive choice. In the case of complex models, or when commercial software is used for the computation without the possibility to change the solver, one indeed needs a non-intrusive method to quantify uncertainties of the model.
Within this project the focus here is to ease the computational burden of the MC type of methods and to rather use stochastic functional approximations of the uncertain parameters or uncertain fields and state variables. The approximation is done with the help of polynomials (general polynomial chaos expansion), or with other approximating functions such as radial basis functions or neural networks. With the help of this proxy modeling the stochastic space is discretized. This discretized representation can be identified also with non-intrusive approaches and enables cheap evaluations of statistics and sampling free approaches to probabilistic parameter identification.
Publikationen im Rahmen des GRK:
Veröffentlichungen in wissenschaftlichen Zeitschriften mit review:
K. Pradeep, N. Friedman, E. Zandera and R. Radespiel. Bayesian Calibration of Volume Averaged RANS Model Parameters for Turbulen Flow Simulations Over Porous Materials. New Results in Numerical and Experimental Fluid Mechanics XI, Springer Verlag, pp 479-488, 2018.[ DOI ]
F. Marsili, P. Croce, N. Friedman, P. Fomichi and P. Landi: Seismic Reliability Assessment of a Concrete Water Tank Based on the Bayesian Updating of the Finite Element Model. Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering3.2 (2017), pp. 67-73.[ DOI ]
Konferenzbeiträge mit Veröffentlichung:
N. Friedman and E. Zander. Stochastic Analysis and Robust Optimization of a Reduced Order Model for Flow Control. SIAM Conference on Uncertainty Quantification, 16-19 April 2018, Garden Grove, CA USA. 2018.[ SIAM ]
P. Croce, P. Formichi, F. Landi, F. Marsili and N. Friedman. Effect of climate change on snow load on ground: Bayesian approach for snow map refinement. 14th International Probabilistic Workshop (pp. 231-244). Springer, Cham. 2017.
S. Dobrilla, N. Friedman, T. Rukavina, H.G. Matthies and A. Ibrahimbegovic. Probabilistic Analysis of Fiber Reinforced Concrete. Proceedings of the CILAMCE 2018 conference; Paris/ Compiègne, France (2018).
P. Kumar, N. Friedman, E. Zander and R. Radespiel. Bayesian Calibration of Volume Averaged RANS Model Parameters for Turbulent Flow Simulations Over Porous Materials. New Results in Numerical and Experimental Fluid Mechanics XI: Contributions to the 20th STAB/DGLR Symposium Braunschweig, Germany, 2016. Ed. by A. Dillmann, G. Heller, E. Krämer, C. Wagner, S. Bansmer, R. Radespiel, and R. Semaan. Cham: Springer International Publishing, 2017, pp. 479-488.[ DOI ]
F. Landi, F. Marsili, N. Friedman, and P. Croce. A comparison of stochastic inverse methods with sampling and functional based linear and non-linear update procedures. Beton und Stahlbau, Extended Abstracts of the 16th International Probabilistic Workshop 2018 in Vienna.