PD Dr. René Henrion

Projects as a project leader

• SE13

  Topology optimization of wind turbines under uncertainties

  Dr. Martin Eigel / PD Dr. René Henrion / Prof. Dr. Dietmar Hömberg / Prof. Dr. Reinhold Schneider

  Project heads: Dr. Martin Eigel / PD Dr. René Henrion / Prof. Dr. Dietmar Hömberg / Prof. Dr. Reinhold Schneider
  Project members: Dr. Johannes Neumann / Dr. Thomas Petzold
  Duration: -
  Status: completed
  Located at: Technische Universität Berlin / Weierstraß-Institut
  

  Description

  The application focus of this project is the topology optimization of the main frame of wind turbines. This is the central assembly platform at the tower head accommodating the drive train, the generator carrier, the azimuth bearing and drives and a lot of small components. Topology optimization should not be mistaken for legally mandated structural analysis computations. For the latter, it is standard to solicit a number of single load scenarios based on available time series data. While this approach is questionable already for stress analysis, it is prohibitive for topology optimization. Disregarding the multivariate distribution of the random loads would not provide any probabilistic certificate for bounding stresses. Moreover, the natural way to choose weights is to derive a stochastic load from available time series data. The main frame is made of cast iron which is prone to a number of material impurities like shrink holes, dross, and chunky graphite. This motivates the additional consideration of randomness for the material stiffness. Structures resulting from topology optimization often exhibit unacceptably high stresses necessitating costly subsequent shape design works. To avoid this already during the optimization, state constraints have to be included in the optimization problem. The main novelty of this project is that it combines a phase field relaxed topology optimisation problem not only with uncertain loading and material data but also with chance state constraints. Even in the finite-dimensional case, the derivation of optimality conditions including gradient formulas is completely open. In the long run, including an appropriate damage model as additional state equation will be a further task of great practical importance.
  
  http://www.wias-berlin.de/projects/ECMath-SE13/

• MI-AP8

  Nonlinear chance constraints in gas transportation problems

  PD Dr. René Henrion

  Project heads: PD Dr. René Henrion
  Project members: -
  Duration: 01.10.2014 - 30.06.2022
  Status: running
  Located at: Weierstraß-Institut
  

  Description

  The aim of this project consists in applying nonlinear probabilistic constraints to optimization problems in gas transportation assuming that the underlying random parameter obeys a multivariate and continuous distribution. Doing so, a robust in the sense of probability design of gas transport shall be facilitated. Stochastic optimization is the appropriate mathematical discipline to cope with uncertainty when looking for optimal decisions under random perturbations of some nominal parameters. Among different modeling options, probabilistic constraints hold a key position first of all in engineering applications. The solution of optimization problems with nonlinear probabilistic constraints with continuous multivariate distributions can be considered as new ground both from the theoretical and – at least for interesting dimension - from the numerical perspectives. Moreover, in the present project, we deal with implicit probabilistic constraints where the relation between decision and random parameter is established only by additional variables via some equation system. Although gas network problems with uncertain injection and consumption provide a very natural motivation for the research in this project, the mathematical insight to be expected has an impact on quite different applications as well, for instance, on optimization problems of power management, particularly those related with renewable energies. Beyond this, optimal control problems governed by PDEs and subjected to random state constraints promise being a potential application of implicit probabilistic constraints. In its first phase the project will investigate optimization problems arising from a simple stationary gas network model (RNET-ISO4) subject to random loads. Here the probabilistic constraint ensures the technical feasibility of loads with a specified probability. In the longer perspective, the consideration of dynamic probabilistic constraints for time-dependent decisions and of binary variables shall be pursued.
  
  http://trr154.fau.de/index.php/en/subprojects/b04e