Tristan Gally

Technical University of Darmstadt

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Marc E. Pfetsch

Technical University of Darmstadt

Pascal Breil

Forum Réfugiés - Cosi

Yuji Shinano

Zuse Institute Berlin

Stefan Ulbrich

Technical University of Darmstadt

Thorsten Koch

Zuse Institute Berlin

Daniel Rehfeldt

Zuse Institute Berlin

Matthias Miltenberger

Zuse Institute Berlin

Gerald Gamrath

Zuse Institute Berlin

Christian Puchert

RWTH Aachen University

Anja Kuttich

Technical University of Darmstadt

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Technical University of Darmstadt

Zuse Institute Berlin

Technische Universität Berlin

RWTH Aachen University

Materials Science & Engineering

Heidelberg University

Darmstadt University of Applied Sciences

University Hospital Heidelberg

Humboldt-Universität zu Berlin

Friedrich-Alexander-Universität Erlangen-Nürnberg

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Identification of model uncertainty via optimal design of experiments applied to a mechanical press

Optimization and Engineering (2021)

Tristan Gally Peter Groche Florian Hoppe Anja Kuttich Alexander Matei

Abstract In engineering applications almost all processes are described with the help of models. Especially forming machines heavily rely on mathematical models for control and condition monitoring. Inaccuracies during the modeling, manufacturing and assembly of these machines induce model uncertainty which impairs the controller’s performance. In this paper we propose an approach to identify model uncertainty using parameter identification, optimal design of experiments and hypothesis testing. The experimental setup is characterized by optimal sensor positions such that specific model parameters can be determined with minimal variance. This allows for the computation of confidence regions in which the real parameters or the parameter estimates from different test sets have to lie. We claim that inconsistencies in the estimated parameter values, considering their approximated confidence ellipsoids as well, cannot be explained by data uncertainty but are indicators of model uncertainty. The proposed method is demonstrated using a component of the 3D Servo Press, a multi-technology forming machine that combines spindles with eccentric servo drives.

Identification

Uncertainty Quantification

Ellipsoid

Sensitivity Analysis

10.1007/s11081-021-09600-8

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Citations (10)

Strategies for Mastering Uncertainty

Springer tracts in mechanical engineering (2021)

Marc E. Pfetsch Eberhard Abele Lena C. Altherr Christian Bölling Nicolas Brötz

Abstract This chapter describes three general strategies to master uncertainty in technical systems: robustness, flexibility and resilience. It builds on the previous chapters about methods to analyse and identify uncertainty and may rely on the availability of technologies for particular systems, such as active components. Robustness aims for the design of technical systems that are insensitive to anticipated uncertainties. Flexibility increases the ability of a system to work under different situations. Resilience extends this characteristic by requiring a given minimal functional performance, even after disturbances or failure of system components, and it may incorporate recovery. The three strategies are described and discussed in turn. Moreover, they are demonstrated on specific technical systems.

Robustness

Resilience

10.1007/978-3-030-78354-9_6

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Citations (1)

« Contexte pédoclimatique et ruissellement intense »

HAL (Le Centre pour la Communication Scientifique Directe) (2022)

Pascal Breil Hélène Abekhzer Tristan Gally

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Robust Truss Topology Design with Beam Elements via Mixed Integer Nonlinear Semidefinite Programming

Applied Mechanics and Materials (2015)

Tristan Gally Christopher M. Gehb Philip Kolvenbach Anja Kuttich Marc E. Pfetsch

In this article, we propose a nonlinear semidefinite program (SDP) for the robust trusstopology design (TTD) problem with beam elements. Starting from the semidefinite formulation ofthe robust TTD problem we derive a stiffness matrix that can model rigid connections between beams.Since the stiffness matrix depends nonlinearly on the cross-sectional areas of the beams, this leads toa nonlinear SDP. We present numerical results using a sequential SDP approach and compare them toresults obtained via a general method for robust PDE-constrained optimization applied to the equationsof linear elasticity. Furthermore, we present two mixed integer semidefinite programs (MISDP), onefor the optimal choice of connecting elements, which is nonlinear, and one for the correspondingproblem with discrete cross-sectional areas.

Semidefinite Programming

Semidefinite embedding

Topology optimization

Matrix (chemical analysis)

10.4028/www.scientific.net/amm.807.229

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Citations (9)

Pedo-climatic context and intense runoff

Pascal Breil Hélène Abekhzer Tristan Gally

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4.1.4 : Améliorations de la méthode IRIP au niveau national

Pascal Breil Tristan Gally

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The SCIP Optimization Suite 6.0

Ambros Gleixner Michael Bastubbe Leon Eifler Tristan Gally Gerald Gamrath

The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. This paper discusses enhancements and extensions contained in version 6.0 of the SCIP Optimization Suite. Besides performance improvements of the MIP and MINLP core achieved by new primal heuristics and a new selection criterion for cutting planes, one focus of this release are decomposition algorithms. Both SCIP and the automatic decomposition solver GCG now include advanced functionality for performing Benders’ decomposition in a generic framework. GCG’s detection loop for structured matrices and the coordination of pricing routines for Dantzig-Wolfe decomposition has been significantly revised for greater flexibility. Two SCIP extensions have been added to solve the recursive circle packing problem by a problem-specific column generation scheme and to demonstrate the use of the new Benders’ framework for stochastic capacitated facility location. Last, not least, the report presents updates and additions to the other components and extensions of the SCIP Optimization Suite: the LP solver SoPlex, the modeling language Zimpl, the parallelization framework UG, the Steiner tree solver SCIP-Jack, and the mixed-integer semidefinite programming solver SCIP-SDP.

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Heuristics

Column generation

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Citations (109)

A framework for solving mixed-integer semidefinite programs

Optimization methods & software (2017)

Tristan Gally Marc E. Pfetsch Stefan Ulbrich

Mixed-integer semidefinite programs (MISDPs) arise in many applications and several problem-specific solution approaches have been studied recently. In this paper, we investigate a generic branch-and-bound framework for solving such problems. We first show that strict duality of the semidefinite relaxations is inherited to the subproblems. Then solver components such as dual fixing, branching rules, and primal heuristics are presented. We show the applicability of an implementation of the proposed methods on three kinds of problems. The results show the positive computational impact of the different solver components, depending on the semidefinite programming solver used. This demonstrates that practically relevant MISDPs can successfully be solved using a general purpose solver.

Solver

Semidefinite Programming

Heuristics

Semidefinite embedding

Duality (order theory)

10.1080/10556788.2017.1322081

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Citations (72)