TY - JOUR A1 - Hintermüller, Michael A1 - Strogies, Nikolai T1 - Identification of the friction function in a semilinear system for gas transport through a network JF - Optimization Methods and Software N2 - An identification problem for the friction parameter in a semilinear system of balance laws, describing the transport of gas through a passive network of pipelines, is considered. The existence of broad solutions to the state system is proven and sensitivity results for the corresponding solution operator are obtained. The existence of solutions to the output least squares formulation of the identification problem, based on noisy measurements over time at fixed spatial positions is established. Finally, numerical experiments validate the theoretical findings. Y1 - 2017 VL - 35 SP - 576 EP - 617 ER - TY - JOUR A1 - Heitsch, Holger A1 - Strogies, Nikolai T1 - Consequences of uncertain friction for the transport of natural gas through passive networks of pipelines JF - Springer N2 - Assuming a pipe-wise constant structure of the friction coefficient in the modeling of natural gas transport through a passive network of pipes via semilinear systems of balance laws with associated linear coupling and boundary conditions, uncertainty in this parameter is quantified by a Markov chain Monte Carlo method. Information on the prior distribution is obtained from practitioners. The results are applied to the problem of validating technical feasibility under random exit demand in gas transport networks. The impact of quantified uncertainty to the probability level of technical feasible exit demand situations is studied by two example networks of small and medium size. The gas transport of the network is modeled by stationary solutions that are steady states of the time dependent semilinear problems. KW - uncertainty quantification, Markov chain Monte Carlo, reliability of gas networks, nomination validation, spheric-radial decomposition Y1 - 2019 SP - 211 EP - 238 ET - Topics in Applied Analysis and Optimisation ER - TY - JOUR A1 - Hajian, Soheil A1 - Hintermüller, Michael A1 - Schillings, Claudia A1 - Strogies, Nikolai T1 - A Bayesian approach to parameter identification in gas networks JF - Control and Cybernetics N2 - The inverse problem of identifying the friction coefficient in an isothermal semilinear Euler system is considered. Adopting a Bayesian approach, the goal is to identify the distribution of the quantity of interest based on a finite number of noisy measurements of the pressure at the boundaries of the domain. First well-posedness of the underlying non-linear PDE system is shown using semigroup theory, and then Lipschitz continuity of the solution operator with respect to the friction coefficient is established. Based on the Lipschitz property, well-posedness of the resulting Bayesian inverse problem for the identification of the friction coefficient is inferred. Numerical tests for scalar and distributed parameters are performed to validate the theoretical results. Y1 - 2018 VL - 48 SP - 377 EP - 402 ER - TY - JOUR A1 - Hintermüller, Michael A1 - Strogies, Nikolai T1 - On the consistency of Runge--Kutta methods up to order three applied to the optimal control of scalar conservation laws JF - Numerical Analysis and Optimization N2 - Higher-order Runge-Kutta (RK) time discretization methods for the optimal control of scalar conservation laws are analyzed and numerically tested. The hyperbolic nature of the state system introduces specific requirements on discretization schemes such that the discrete adjoint states associated with the control problem converge as well. Moreover, conditions on the RK-coefficients are derived that coincide with those characterizing strong stability preserving Runge-Kutta methods. As a consequence, the optimal order for the adjoint state is limited, e.g., to two even in the case where the conservation law is discretized by a third-order method. Finally, numerical tests for controlling Burgers equation validate the theoretical results. Y1 - 2017 U6 - https://doi.org/10.20347/WIAS.PREPRINT.2442 SP - 119 EP - 154 ER - TY - JOUR A1 - Hintermüller, Michael A1 - Rautenberg, Carlos A1 - Strogies, Nikolai T1 - Dissipative and Non-dissipative Evolutionary Quasi-variational Inequalities with Gradient Constraints JF - Set-Valued and Variational Analysis N2 - Evolutionary quasi-variational inequality (QVI) problems of dissipative and non-dissipative nature with pointwise constraints on the gradient are studied. A semi-discretization in time is employed for the study of the problems and the derivation of a numerical solution scheme, respectively. Convergence of the discretization procedure is proven and properties of the original infinite dimensional problem, such as existence, extra regularity and non-decrease in time, are derived. The proposed numerical solver reduces to a finite number of gradient-constrained convex optimization problems which can be solved rather efficiently. The paper ends with a report on numerical tests obtained by a variable splitting algorithm involving different nonlinearities and types of constraints. Y1 - 2017 VL - 27 SP - 433 EP - 468 ER - TY - JOUR A1 - Egger, Herbert A1 - Kugler, Thomas A1 - Strogies, Nikolai T1 - Parameter identification in a semilinear hyperbolic system JF - Inverse Problems N2 - We consider the identification of a nonlinear friction law in a one-dimensional damped wave equation from additional boundary measurements. Well-posedness of the governing semilinear hyperbolic system is established via semigroup theory and con- traction arguments. We then investigte the inverse problem of recovering the unknown nonlinear damping law from additional boundary measurements of the pressure drop along the pipe. This coefficient inverse problem is shown to be ill-posed and a varia- tional regularization method is considered for its stable solution. We prove existence of minimizers for the Tikhonov functional and discuss the convergence of the regularized so- lutions under an approximate source condition. The meaning of this condition and some arguments for its validity are discussed in detail and numerical results are presented for illustration of the theoretical findings Y1 - 2016 VL - 33 IS - 055022 ER -