2–3 PM — Felix Schneider (Technical University of Münich) — [slides]
Sparse Bayesian Learning for Rational Polynomial Chaos Expansion and Application in Structural DynamicsSurrogate models enable efficient propagation of uncertainties in computationally demanding models of physical systems. We employ surrogate models that draw upon polynomial bases to model the stochastic frequency response of structural dynamics systems subject to parameter uncertainty. Therein, we define a rational polynomial chaos expansion (rPCE) as the ratio of two polynomial chaos expansions. The rPCE is thereby specifically suitable for models that include poles in the system response. We apply least squares and Bayesian regression techniques to determine the numerator and denominator coefficients, which allows straightforward coupling of the proposed methods with existing black-box solvers. This webinar focusses on a sparse Bayesian learning approach for the determination of the surrogate model coefficients in the rPCE. Due to the non-linearity of the surrogate with respsect to the denominator coefficients, we resort to a sequential solution strategy that utilizes the availability of a closed-form solution for the posterior distribution of the numerator coefficients. Subsequently, Laplace’s approximation is used to approximate the posterior distribution of the denominator coefficients. The coefficients and an optimal set of hyperparameters are then found in a sequential manner. We compare the performance with previously proposed strategies, which do not consider the uncertainty related to the denominator coefficients. Joint work with Iason Papaioannou & Gerhard Müller References:
- F. Schneider, I. Papaioannou, M. Ehre and D. Straub. Polynomial chaos based rational approximation in linear structural dynamics with parameter uncertainties. Computers & Structures 233, 2020.
- F. Schneider, I. Papaioannou, G. Müller, Sparse Bayesian Learning for Complex‐Valued Rational Approximations. International Journal for Numerical Methods in Engineering, 2022.
- F. Schneider, I. Papaioannou, D. Straub, C. Winter, G. Müller, Bayesian parameter updating in linear structural dynamics with frequency transformed data using rational surrogate models. Mechanical Systems and Signal Processing 166, 2022.
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