Showing papers by "Marc E. Pfetsch published in 2021"

Mastering Uncertainty in Mechanical Engineering

Abstract: This open access book reports on innovative methods, technologies and strategies for mastering uncertainty in technical systems. Despite the fact that current research on uncertainty is mainly focusing on uncertainty quantification and analysis, this book gives emphasis to innovative ways to master uncertainty in engineering design, production and product usage alike. It gathers authoritative contributions by more than 30 scientists reporting on years of research in the areas of engineering, applied mathematics and law, thus offering a timely, comprehensive and multidisciplinary account of theories and methods for quantifying data, model and structural uncertainty, and of fundamental strategies for mastering uncertainty. It covers key concepts such as robustness, flexibility and resilience in detail. All the described methods, technologies and strategies have been validated with the help of three technical systems, i.e. the Modular Active Spring-Damper System, the Active Air Spring and the 3D Servo Press, which have been in turn developed and tested during more than ten years of cooperative research. Overall, this book offers a timely, practice-oriented reference guide to graduate students, researchers and professionals dealing with uncertainty in the broad field of mechanical engineering.

Combinatorial acyclicity models for potential‐based flows

Abstract: Potential-based flows constitute a basic model to represent physical behavior in networks. Under natural assumptions, the flow in such networks must be acyclic. The goal of this paper is to exploit this property for the solution of corresponding optimization problems. To this end, we introduce several combinatorial models for acyclic flows, based on binary variables for flow directions. We compare these models and introduce a particular model that tries to capture acyclicity together with the supply/demand behavior. We analyze properties of this model, including variable fixing rules. Our computational results show that the usage of the corresponding constraints speeds up solution times by about a factor of 3 on average and a speed-up of a factor of almost 5 for the time to prove optimality.

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

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.

Estimating the Size of Branch-and-Bound Trees

Abstract: This paper investigates the problem of estimating the size of branch-and-bound (B&B) trees for solving mixed-integer programs. We first prove that the size of the B&B tree cannot be approximated wi...

Types of Uncertainty

Abstract: The goal of this chapter is to define different types of uncertainty in technical systems and to provide a unified terminology for this book. Indeed, uncertainty comes in different disguises. The first distinction is made with respect to the knowledge on the source of uncertainty: stochastic uncertainty, incertitude or ignorance. Then three main occurrences of uncertainty are discussed: data, model and structural uncertainty.

Optimal patchings for consecutive ones matrices

Abstract: We study a variant of the weighted consecutive ones property problem. Here, a 0/1-matrix is given with a cost associated to each of its entries and one has to find a minimum cost set of zero entries to be turned to ones in order to make the matrix have the consecutive ones property for rows. We investigate polyhedral and combinatorial properties of the problem and we exploit them in a branch-and-cut algorithm. In particular, we devise preprocessing rules and investigate variants of “local cuts”. We test the resulting algorithm on a number of instances, and we report on these computational experiments.

Recovery under Side Constraints

Abstract: This paper addresses sparse signal reconstruction under various types of structural side constraints with applications in multi-antenna systems. Side constraints may result from prior information on the measurement system and the sparse signal structure. They may involve the structure of the sensing matrix, the structure of the non-zero support values, the temporal structure of the sparse representationvector, and the nonlinear measurement structure. First, we demonstrate how a priori information in form of structural side constraints influence recovery guarantees (null space properties) using L1-minimization. Furthermore, for constant modulus signals, signals with row-, block- and rank-sparsity, as well as non-circular signals, we illustrate how structural prior information can be used to devise efficient algorithms with improved recovery performance and reduced computational complexity. Finally, we address the measurement system design for linear and nonlinear measurements of sparse signals. Moreover, we discuss the linear mixing matrix design based on coherence minimization. Then we extend our focus to nonlinear measurement systems where we design parallel optimization algorithms to efficiently compute stationary points in the sparse phase retrieval problem with and without dictionary learning.

Schreier-Sims Cuts meet Stable Set: Preserving Problem Structure when Handling Symmetries.

Abstract: Symmetry handling inequalities (SHIs) are a popular tool to handle symmetries in integer programming. Despite their successful application in practice, only little is known about the interaction of SHIs with optimization problems. In this article, we focus on SST cuts, an attractive class of SHIs, and investigate their computational and polyhedral consequences for optimization problems. After showing that they do not increase the computational complexity of solving optimization problems, we focus on the stable set problem for which we derive presolving techniques based on SST cuts. Moreover, we derive strengthened versions of SST cuts and identify cases in which adding these inequalities to the stable set polytope maintains integrality. Preliminary computational experiments show that our techniques have a high potential to reduce both the size of stable set problems and the time to solve them.

Analysis, Quantification and Evaluation of Uncertainty

Abstract: This chapter describes the various approaches to analyse, quantify and evaluate uncertainty along the phases of the product life cycle. It is based on the previous chapters that introduce a consistent classification of uncertainty and a holistic approach to master the uncertainty of technical systems in mechanical engineering. Here, the following topics are presented: the identification of uncertainty by modelling technical processes, the detection and handling of data-induced conflicts, the analysis, quantification and evaluation of model uncertainty as well as the representation and visualisation of uncertainty. The different approaches are discussed and demonstrated on exemplary technical systems.

Our Specific Approach on Mastering Uncertainty

Abstract: This chapter serves as an introduction to the main topic of this book, namely to master uncertainty in technical systems. First, the difference of our approach to previous ones is highlighted. We then discuss process chains as an important type of technical systems, in which uncertainty propagates along the chain. Five different approaches to master uncertainty in process chains are presented: uncertainty identification, uncertainty propagation, robust optimisation, sensitivity analysis and model adaption. The influence of the process on uncertainty and methods depends on whether it is dynamic/time-varying and/or active. This brings us to the main strategies for mastering uncertainty: robustness, flexibility and resilience. Finally, three different concrete technical systems that are used to demonstrate our methods are presented.

Validation of an Optimized Resilient Water Supply System

Abstract: Component failures within water supply systems can lead to significant performance losses One way to address these losses is the explicit anticipation of failures within the design process We consider a water supply system for high-rise buildings, where pump failures are the most likely failure scenarios We explicitly consider these failures within an early design stage which leads to a more resilient system, ie, a system which is able to operate under a predefined number of arbitrary pump failures We use a mathematical optimization approach to compute such a resilient design This is based on a multi-stage model for topology optimization, which can be described by a system of nonlinear inequalities and integrality constraints Such a model has to be both computationally tractable and to represent the real-world system accurately We therefore validate the algorithmic solutions using experiments on a scaled test rig for high-rise buildings The test rig allows for an arbitrary connection of pumps to reproduce scaled versions of booster station designs for high-rise buildings We experimentally verify the applicability of the presented optimization model and that the proposed resilience properties are also fulfilled in real systems

Packing under convex quadratic constraints

Abstract: We consider a general class of binary packing problems with a convex quadratic knapsack constraint. We prove that these problems are APX-hard to approximate and present constant-factor approximation algorithms based upon three different algorithmic techniques: (1) a rounding technique tailored to a convex relaxation in conjunction with a non-convex relaxation whose approximation ratio equals the golden ratio; (2) a greedy strategy; (3) a randomized rounding method leading to an approximation algorithm for the more general case with multiple convex quadratic constraints. We further show that a combination of the first two strategies can be used to yield a monotone algorithm leading to a strategyproof mechanism for a game-theoretic variant of the problem. Finally, we present a computational study of the empirical approximation of the three algorithms for problem instances arising in the context of real-world gas transport networks.

Strategies for Mastering Uncertainty

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.

Ambiguities in Direction-of-Arrival Estimation with Linear Arrays

Abstract: In this paper, we present a novel approach to compute ambiguities in thinned uniform linear arrays, i.e., sparse non-uniform linear arrays, via a mixed-integer program. Ambiguities arise when there exists a set of distinct directions-of-arrival, for which the corresponding steering matrix is rank-deficient and are associated with nonunique parameter estimation. Our approach uses Young tableaux for which a submatrix of the steering matrix has a vanishing determinant, which can be expressed through vanishing sums of unit roots. Each of these vanishing sums then corresponds to an ambiguous set of directions-of-arrival. We derive a method to enumerate such ambiguous sets using a mixed-integer program and present results on several examples.