| Autor(en) | Kumar, Pradeep | Friedman, Noémi | Zander, Elmar | Radespiel, Rolf | Kumar, Pradeep |
|---|---|
| Titel | Bayesian Calibration of Volume Averaged RANS Model Parameters for Turbulent Flow Simulations Over Porous Materials |
| Herausgeber | New Results in Numerical and Experimental Fluid Mechanics XI, Springer Verlag, pp 479-488, 2018 |
| Erscheinungsjahr | 2018 |
| Abstract | A mathematical tool developed for calibrating model parameters of VRANS equations for modeling flows through porous medium is evaluated. A total of six parameters are introduced in a volume averaged RANS model to appropriately scale the impact of porous media on the overall flow. The calibration tool has been tested for a generic channel case and the results are compared with DNS simulations of the same. The results show a good agreement between the parameters obtained from the tool and a manual calibration documented previously. |
| Autor(en) | Loukrezis, Dimitrios | Römer, Ulrich | Casper, Thorben | Schöps, Sebastian | De Gersem, Herbert |
|---|---|
| Titel | High-dimensional uncertainty quantification for an electrothermal field problem using stochastic collocation on sparse grids and tensor train decompositions |
| Herausgeber | International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, Vol. 31 |
| Erscheinungsjahr | 2018 |
| Abstract | The temperature developed in bondwires of integrated circuits (ICs) is a possible source of malfunction and has to be taken into account during the design phase of an IC. Because of manufacturing tolerances, a bondwire’s geometrical characteristics are uncertain parameters, and as such, their impact has to be examined with the use of uncertainty quantification methods. Considering a stochastic electrothermal problem featuring 12 bondwire-related uncertainties, we want to quantify the impact of the uncertain inputs onto the temperature developed during the duty cycle of an IC. For this reason, we apply the stochastic collocation method on sparse grids, which is considered the current state-of-the-art. We also implement an approach based on the recently introduced low-rank tensor decompositions, in particular the tensor train decomposition, which in theory promises to break the curse of dimensionality. A comparison of both methods is presented, with respect to accuracy and computational effort. |
| Autor(en) | Rang, Joachim | Heinze, Wolfgang |
|---|---|
| Titel | An Optimal Configuration of an Aircraft with High Lift Configuration Using Surrogate Models and Optimisation Under Uncertainties |
| Herausgeber | Advances in Structural and Multidisciplinary Optimization In: Schumacher A., Vietor T., Fiebig S., Bletzinger KU., Maute K. (eds) Advances in Structural and Multidisciplinary Optimization. WCSMO 2017. Springer, Cham |
| Erscheinungsjahr | 2018 |
| Abstract | Nowadays many simulations are computationally expensive, which is disadvantageous if one is interested in the quantification of uncertainties, parameter studies or in finding an optimal or robust design. Therefore often so-called surrogate models are designed, which are a good approximation of the original model but computationally less expensive. In this paper we first look for an approximation method to design a surrogate model for the simulation of a civil aircraft with active high lift configuration. Such aircrafts have the advantage that only small runways for take-off and landing are necessary. A first result, presented in this paper, is a configuration of the aircraft, where the direct operating costs (DOCs) are minimised. For the optimisation process seven parameters are chosen, for example the Mach number in the cruise flight and the area of the wing. In a second step we define 28 uncertain parameters and repeat the optimisation process including these uncertain parameters to derive a robust configuration. |
| Autor(en) | Rang, Joachim | Heinze, Wolfgang |
|---|---|
| Titel | An Optimal Configuration of an Aircraft with High Lift Configuration Using Surrogate Models and Optimisation Under Uncertainties |
| Herausgeber | Advances in Structural and Multidisciplinary Optimization, Springer International Publishing AG, 2018 |
| Erscheinungsjahr | 2018 |
| Abstract | Nowadays many simulations are computationally expensive, which is disadvantageous if one is interested in the quantification of uncertainties, parameter studies or in finding an optimal or robust design. Therefore often so-called surrogate models are designed, which are a good approximation of the original model but computationally less expensive. In this paper we first look for an approximation method to design a surrogate model for the simulation of a civil aircraft with active high lift configuration. Such aircrafts have the advantage that only small run-ways for take-off and landing are necessary. A first result, presented in this paper, is a configuration of the aircraft, where the direct operating costs (DOCs) are minimised. For the optimisation process seven parameters are chosen, for example the Mach number in the cruise flight and the area of the wing. In a second step we define 28 uncertain parameters and repeat the optimisation process including these uncertain parameters to derive a robust configuration. |
| Autor(en) | Römer, Ulrich | Narayanamurthi, Mahesh | Sandu, Adrian |
|---|---|
| Titel | Solving parameter estimation problems with discrete adjoint exponential integrators |
| Herausgeber | Optimization Methods and Software, DOI: 10.1080/10556788.2018.1448087, in print |
| Erscheinungsjahr | 2018 |
| Abstract | The solution of inverse problems in a variational setting finds best estimates of the model parameters by minimizing a cost function that penalizes the mismatch between model outputs and observations. The gradients required by the numerical optimization process are computed using adjoint models. Exponential integrators are a promising family of time discretization schemes for evolutionary partial differential equations. In order to allow the use of these discretization schemes in the context of inverse problems, adjoints of exponential integrators are required. This work derives the discrete adjoint formulae for W-type exponential propagation iterative methods of Runge–Kutta type (EPIRK-W). These methods allow arbitrary approximations of the Jacobian while maintaining the overall accuracy of the forward integration. The use of Jacobian approximation matrices that do not depend on the model state avoids the complex calculation of Hessians in the discrete adjoint formulae. The adjoint code itself is generated efficiently via algorithmic differentiation and used to solve inverse problems with the Lorenz-96 model and a model from computational magnetics. Numerical results are encouraging and indicate the suitability of exponential integrators for this class of problems. |
| Autor(en) | Loukrezis, Dimitrios | Römer, Ulrich | De Gersem, Herbert |
|---|---|
| Titel | Numerical Comparison of Leja and Clenshaw-Curtis Dimension-Adaptive Collocation for Stochastic Parametric Electromagnetic Field Problems |
| Herausgeber | ARXIV Preprint, arXiv:1712.07223v1 |
| Erscheinungsjahr | 2017 |
| Abstract | We consider the problem of approximating the output of a parametric electromagnetic field model in the presence of a large number of uncertain input parameters. Given a sufficiently smooth output with respect to the input parameters, such problems are often tackled with interpolation-based approaches, such as the stochastic collocation method on tensor-product or isotropic sparse grids. Due to the so-called curse of dimensionality, those approaches result in increased or even forbidding computational costs. In order to reduce the growth in complexity with the number of dimensions, we employ a dimension-adaptive, hierarchical interpolation scheme, based on nested univariate interpolation nodes. Clenshaw-Curtis and Leja nodes satisfy the nestedness property and have been found to provide accurate interpolations when the parameters follow uniform distributions. The dimension-adaptive algorithm constructs the approximation based on the observation that not all parameters or interactions among them are equally important regarding their impact on the model’s output. Our goal is to exploit this anisotropy in order to construct accurate polynomial surrogate models at a reduced computational cost compared to isotropic sparse grids. We apply the stochastic collocation method to two electromagnetic field models with medium- to high-dimensional input uncertainty. The performances of isotropic and adaptively constructed, anisotropic sparse grids based on both Clenshaw-Curtis and Leja interpolation nodes are examined. All considered approaches are compared with one another regarding the surrogate models’ approximation accuracies using a cross-validation error metric. |
| Autor(en) | Friedman, Noemi | Kumar, Pradeep | Zander, Elmar | Matthies, Hermann G. |
|---|---|
| Titel | Bayesian calibration of model coefficients for a simulation of flow over porous material involving SVM classification |
| Herausgeber | PAMM (Proceedings in Applied Mathematics and Mechanics), Vol 16. Issue 1, 016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim, pp 669-670, GAMM Braunschweig, 2016 |
| Erscheinungsjahr | 2016 |
| Abstract | n this contribution the identification of the model coefficients of a novel turbulent flow model over porous media is concerned. The flow is modeled with a volume and Reynolds averaged compressible Navier‐Stokes equations approach. The main focus of this contribution is to calibrate the model coefficients starting from expert prior knowledge by incorporating DNS data of the velocity field and the Reynolds stresses. For the inverse problem general Polynomial Chaos Expansions (gPCE) based surrogate model was used. To avoid the identification of nonphysical coefficient setups, these parametric regions were filtered out by identifying a decision boundary by the support vector machine binary classification. The machinery of the Markov Chain Monte Carlo (MCMC) was used for the data assimilation combined with a nonlinear Minimum Mean Square Estimator (MMSE) for speeding up the convergence of the random walk of the MCMC. |
| Autor(en) | Matthies, Hermann G. | Litvinenko, Alexander | Rosic, Bojana V. | Zander, Elmar |
|---|---|
| Titel | Bayesian Parameter Estimation via Filtering and Functional Approximations |
| Herausgeber | ARXIV Preprint, arXiv:1611.09293 |
| Erscheinungsjahr | 2016 |
| Abstract | The inverse problem of determining parameters in a model by comparing some output of the model with observations is addressed. This is a description for what hat to be done to use the Gauss-Markov-Kalman filter for the Bayesian estimation and updating of parameters in a computational model. This is a filter acting on random variables, and while its Monte Carlo variant — the Ensemble Kalman Filter (EnKF) — is fairly straightforward, we subsequently only sketch its implementation with the help of functional representations. |
| Autor(en) | Matthies, Hermann G. | Zander, Elmar | Rosic, Bojana V. | Litvinenko, Alexander |
|---|---|
| Titel | Parameter estimation via conditional expectation: a Bayesian inversion |
| Herausgeber | Advanced Modeling and Simulation in Engineering Sciences, 3:24, 2016 |
| Erscheinungsjahr | 2016 |
| Abstract | When a mathematical or computational model is used to analyse some system, it is usual that some parameters resp. functions or fields in the model are not known, and hence uncertain. These parametric quantities are then identified by actual observations of the response of the real system. In a probabilistic setting, Bayes’s theory is the proper mathematical background for this identification process. The possibility of being able to compute a conditional expectation turns out to be crucial for this purpose. We show how this theoretical background can be used in an actual numerical procedure, and shortly discuss various numerical approximations. |
| Autor(en) | Matthies, Hermann G. | Zander, Elmar | Rosic, Bojana V. | Litvinenko, Alexander | Pajonk, Oliver |
|---|---|
| Titel | Inverse Problems in a Bayesian Setting |
| Herausgeber | Computational Methods for Solids and Fluids, Springer International Publishing Switzerland, pp 245-286, 2016 |
| Erscheinungsjahr | 2016 |
| Abstract | In a Bayesian setting, inverse problems and uncertainty quantification (UQ)—the propagation of uncertainty through a computational (forward) model — are strongly connected. In the form of conditional expectation the Bayesian update becomes computationally attractive.We give a detailed account of this approach via conditional approximation, various approximations, and the construction of filters. Together with a functional or spectral approach for the forward UQ there is no need for time-consuming and slowly convergent Monte Carlo sampling. The developed sampling-free non-linear Bayesian update in form of a filter is derived from the variational problem associated with conditional expectation. This formulation in general calls for further discretisation to make the computation possible, and we choose a polynomial approximation. After giving details on the actual computation in the framework of functional or spectral approximations, we demonstrate the workings of the algorithm on a number of examples of increasing complexity.At last, we compare the linear and nonlinear Bayesian update in form of a filter on some examples. |
| Autor(en) | Römer, Ulrich | Schöps, Sebastian | Weiland, Thomas |
|---|---|
| Titel | Stochastic Modeling and Regularity of the Nonlinear Elliptic curl-curl Equation |
| Herausgeber | SIAM/ASA Journal on Uncertainty Quantification, Vol. 4 |
| Erscheinungsjahr | 2016 |
| Abstract | This paper addresses the nonlinear elliptic curl-curl equation with uncertainties in the material law. It is frequently employed in the numerical evaluation of magnetostatic elds, where the uncertainty is ascribed to the so-called B-H curve. A truncated Karhunen-Loeve approximation of the stochastic B-H curve is presented and analyzed with regard to monotonicity constraints. A stochastic nonlinear curl-curl formulation is introduced and numerically approximated by a nite element and collocation method in the deterministic and the stochastic variable, respectively. The stochastic regularity is analyzed by a higher-order sensitivity analysis. It is shown that, unlike in linear and several nonlinear elliptic problems, the solution is not analytic with respect to the random variables, and an algebraic decay of the stochastic error is obtained. Numerical results for both the Karhunen-Loeve expansion and the stochastic curl-curl equation are given for illustration. |
| Autor(en) | Krosche, Martin | Heinze, Wolfgang |
|---|---|
| Titel | Robustness Analysis of an Aircraft Design for Short Takeoff and Landing |
| Herausgeber | Journal of Aircraft, July, Vol. 52, No. 4 : pp. 1235-1246 |
| Erscheinungsjahr | 2015 |
| Abstract | As part of the Collaborative Research Center 880, preliminary aircraft design activities are carried out for a new class of low-noise cruise-efficient short takeoff and landing (CESTOL) transport aircraft. A corresponding aircraft is quite different from a state-of-the-art commercial aircraft because of the use of a high-lift system with active flow control. The fact that new technologies are not sufficiently understood yet in combination with the assumption of common design data and the use of classical calculation methods expresses itself in uncertainties that are of epistemic character. The robustness of a deterministic CESTOL aircraft design toward parameters such as the necessary engine thrust, direct operating costs, and the maximum takeoff and landing distances is investigated here concerning the mentioned uncertainties. For this purpose, a stochastic description of parameter variations of the design is formulated. Stochastic quantities are computed by Monte Carlo sampling to rate the robustness. A distributed component-based software implementation is used to perform the Monte Carlo sampling. The software system is installed on a Linux cluster with several multi-CPU computers, a deterministic sample is simulated through the design program PrADO. |
| Autor(en) | Rosic, Bojana | Diekmann, Jobst |
|---|---|
| Titel | Methods for the Uncertainty Quantification of Aircraft Simulation Models |
| Herausgeber | Journal of Aircraft, Vol. 52, No. 4 (2015), pp. 1247-1255 |
| Erscheinungsjahr | 2015 |
| Abstract | The paper deals with the propagation of uncertainty in input parameters through the aircraft model in clean cruise configuration triggered by the elevator pulse. Assuming aerodynamic coefficients as random variables and processes, the evolution of uncertainties in the aircraft state is estimated with the help of efficient nonintrusive procedures—stochastic collocation and the nonintrusive Galerkin approaches, here contrasted to the slow convergent Monte Carlo integration. These numerical methods are implemented by using the flight simulator in a black-box manner. In this way, the set of samples of aircraft states is simply obtained by solving the corresponding systems of deterministic ordinary differential equations. Additionally, the paper provides the variance-based sensitivity analysis of a flight model carried out with the help of the polynomial-chaos approach. Read More: https://arc.aiaa.org/doi/10.2514/1.C032856 |
| Autor(en) | Krosche, Martin | Heinze, Wolfgang |
|---|---|
| Titel | A Robustness Analysis of a Preliminary Design of a CESTOL Aircraft |
| Herausgeber | Informatikbericht 2014-02, Institut für Wissenschaftliches Rechnen, Carl-Friedrich-Gauß-Fakultät, TU Braunschweig |
| Erscheinungsjahr | 2014 |
| Abstract | As part of the Collaborative Research Center 880 preliminary aircraft design activities are carried out for a new class of low-noise cruise-efficient transport aircrafts with short take-off and landing capabilities (CESTOL). A corresponding aircraft is quite different from a state-of-the-art commercial aircraft because of the use of active high-lift devices. The fact that new technologies are not sufficiently understood yet in combination with the assumption of common design data and the use of classical calculation methods expresses itself in uncertainties which are of epistemic character. The robustness of a deterministic CESTOL aircraft design towards parameters such as the necessary engine thrust, direct operating costs, or the runway lengths is investigated here concerning the mentioned uncertainties. For this purpose a stochastic description of parameter variations of the design is formulated. Stochastic quantities are computed by Monte Carlo (MC) sampling to rate the robustness. A distributed component-based software implementation is used to perform the MC sampling. The software system is installed on a Linux cluster with several multi-CPU computers, a deterministic sample is simulated through the design program PrADO. |
| Autor(en) | Römer, Ulrich | Schöps, Sebastian | Weiland, Thomas |
|---|---|
| Titel | Approximation of Moments for the Nonlinear Magnetoquasistatic Problem with Material Uncertainties |
| Herausgeber | IEEE Transactions on Magnetics, Vol. 50 |
| Erscheinungsjahr | 2014 |
| Abstract | In this paper, we study the magnetoquasistatic problem with uncertainties in the nonlinear magnetic material characteristic. In the case of small input uncertainties, adjoint techniques can be used to efficiently approximate the statistics of the quantities of interest. We carry out the corresponding sensitivity analysis and investigate the method’s approximation properties. Numerical results discussing the approximation error are given for an electrical transformer. |