Uncertainty Quantification and Updating in the Description of Heat and Moisture Transport in Heterogeneous Materials

• Applicant: Professor Dr. Hermann Georg Matthies
• Subject Area: Mechanics ; Security and Dependability, Operating-, Communication- and Distributed Systems
• Term: from 2009 to 2015
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 162182726

• Final Report Year: 2014

Final Report Abstract

The project focused on probabilistic methods for the description of heterogeneous materials, which can be used for the quantification of uncertainty in the structural response, or for the identification of structural model parameters given noisy measurement data. The propagation of uncertainty through the forward model is achieved in an efficient and adaptive way by using stochastic Galerkin procedures. By using these methods we achieved to substitute the computationally expensive forward model with the faster functional approximation variants–the so called proxy model. The introduction of the proxy model to the Bayesian inference has opened new ways to the computation of the posterior. With the help of functional approximation of the considered random variables (fields), we achieved to rewrite the Bayesian inference in terms of projections onto a generalised polynomial chaos basis. In this manner we developed a fully deterministic method to compute sequential updates of stochastic estimates given noisy measurements. Being irrelevant to the type of distribution for either data or measurement this method has shown to be an extensive generalisation of the Kalman type of estimates, especially when higher order terms of the prediction mismatch are taken into account.

Publications

• Parameter Identification in a Probabilistic Setting. Engineering Structures, 50: 179–196, 2013
  B. Rosić, A. Kučerová, J. Sýkora, O. Pajonk, A. Litvinenko and H. G. Matthies
  (See online at https://dx.doi.org/10.1016/j.engstruct.2012.12.029)
• A Deterministic Filter for Non-Gaussian Bayesian Estimation - Applications to Dynamical System Estimation with Noisy Measurements. Physica D: Nonlinear Phenomena, 241(7): 775–788, 2012
  O. Pajonk, B. Rosić, A. Litvinenko and H. G. Matthies
  (See online at https://doi.org/10.1016/j.physd.2012.01.001)
• Acceleration of Uncertainty Updating in the Description of Transport Processes in Heterogeneous Materials. Journal of Computational and Applied Mathematics, 236(18): 4862-4872, 2012
  A. Kučerová, J. Sýkora, B. Rosić and H. G. Matthies
  (See online at https://doi.org/10.1016/j.cam.2012.02.003)
• Sampling Free Bayesian Update of Polynomial Chaos Representations. Journal of Computational Physics, 231 (17): 5761-5787, 2012
  B. Rosić, A. Litvinenko, O. Pajonk and H. G. Matthies
  (See online at https://doi.org/10.1016/j.jcp.2012.04.044)
• Identification of Properties of Stochastic Elastoplastic Systems. In Computational Methods in Applied Sciences: Computational Methods in Stochastic Dynamics, M. Papadrakakis, G. Stefanou, and V. Papadopoulos (Eds.), 26: 237–253, Springer, Dordrecht, 2013
  B. Rosić and H. G. Matthies
  
• Sampling-free Linear Bayesian Updating of Model State and Parameters Using a Square Root Approach. Computers and Geosciences, 55:70-83, 2013
  O. Pajonk, B. Rosić, and H. G. Matthies
  (See online at https://dx.doi.org/10.1016/j.cageo.2012.05.017)