bluuebunny/crossref_metadata_2025_split huggingface dataset:
Analytical approximations for the solution of chance constrained optimization problems
Authors: Klöppel Michael , Geletu Abebe , Hoffmann Armin , Li Pu , Wensch Jörg 
Published: December 2014

AbstractUncertain influences are inherent in many practical processes, stemming for instance from measurement errors in process optimization or missing knowledge about the future behavior of a given system, e.g., the financial markets. Therefore, it is desirable to explicitly consider uncertainties when optimizing such processes. One possible approach for this task is the usage of chance constrained optimization (CCOPT), which allows that the constraints are only held with a certain probability level. This enables the user to make a compromised decision between reliability and profitability. Solving CCOPT problems usually consists of two steps. First, transforming the chance constraints into deterministic ones and then solving the transformed problem with a standard NLP solver. Depending on the underlying process, several approaches exist for the transformation. Here, we investigate the usage of so called analytical approximations (AAs). In general, AA approaches do not lead to an exact deterministic representation of CCOPT problems. Nonetheless, it can be shown that a solution obtained by AA is always feasible for the original problem. Furthermore, the corresponding optimization problem generated by AA is computationally more tractable than the original formulation, making these approaches interesting for larger scale processes. We propose a new AA method and present a comparison with existing AA approaches, considering efficiency and suitability. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On regularization in parameter‐free shape optimization
Authors: Riehl Stefan , Friederich Jan , Steinmann Paul 
Published: December 2014

AbstractThis contribution is concerned with a parameter‐free approach to computational shape optimization of mechanically‐loaded structures. Thereby the term ’parameter‐free’ refers to approaches in shape optimization in which the design variables are not derived from an existing CAD‐parametrization of the model geometry but rather from its finite element discretization. One of the major challenges in using this type of approach is the avoidance of oscillating boundaries in the optimal design trials. This difficulty is mainly attributed to a lack of smoothness of the objective sensitivities and the relatively high number of design variables within the parameter‐free regime. To compensate for these deficiencies, Azegami introduced the concept of the so‐called traction method, in which the actual design update is deduced from the deformation of a fictitious continuum that is loaded in proportion to the negative shape gradient. We investigate a discrete variant of the traction method, in which the design sensitivities are computed with respect to variations of the design nodes for a given finite element mesh rather than on the abstract level by means of the speed method. Moreover, the design update process is accompanied by adaptive mesh refinement based on discrete material residual forces. Therein, we consider radaptive node relocation as well as hadaptive mesh refinement. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Manufacturing constraints in parameter–free shape optimization
Authors: Schmitt Oliver , Friederich Jan , Steinmann Paul 
Published: December 2014

AbstractStructural shape optimization has become an important tool for engineers when it comes to improving components with respect to a given goal function. During this process the designer has to ensure that the optimized part stays manufacturable. Depending on the manufacturing process several requirements could be relevant such as demolding or different kinds of symmetry. This work introduces two approaches on how to handle manufacturing constraints in parameter‐free shape optimization. In the so–called explicit approach equality and inequality equations are formulated using the coordinates of the FE‐nodes. These equations can be used to extend the optimization problem. Since the number of the additional constraint equations may be very large we apply aggregation formulations, e.g. the Kreisselmeier‐Steinhauser function, if necessary. In the second approach, the so–called implicit method, the set of design nodes is split in two groups called optimization nodes and dependent nodes. The optimization nodes are now handled as design nodes but the dependent nodes are coupled to the optimization nodes in such a way that the manufacturing constraint is fulfilled. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A hybrid approach to optimization of trajectories in micro manufacturing
Authors: Bauma Elisabeth , Schuster Thomas 
Published: December 2014

AbstractA new approach for solving optimal control problem with state constraints is introduced. Therein a combination of direct and indirect methods enables the determination of numerical solutions of the problem. As a motivating task the trajectory optimization of a novel feed unit is investigated. As the mechanism contains compliances, small disturbances have to be taken into consideration, this is done by introducing a penalty term to the objective function. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A time transformation technique for Switched Systems Optimal Control Problems with fixed sequence of phases
Authors: Palagachev Konstantin , Gerdts Matthias 
Published: December 2014

AbstractA switched systems optimal control problem regarding a quadcopter trajectory optimization is considered. Introducing a particular time transformation, the problem is reformulated as an optimal control problem, whose solution can be found by the SQP algorithm. A numerical example concludes the paper. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
An LDLT factorization based ADI algorithm for solving large‐scale differential matrix equations
Authors: Lang Norman , Mena Hermann , Saak Jens 
Published: December 2014

AbstractLarge‐scale differential matrix equations appear in many applications like optimal control of partial differential equations, balanced truncation model order reduction of linear time varying systems etc. Here, we will focus on matrix Riccati differential equations (RDE). Solving such matrix valued ordinary differential equations (ODE) is a highly storage and time consuming process. Therefore, it is necessary to develop efficient solution strategies minimizing both. We present an LDLT factorization based ADI method for solving algebraic Lyapunov equations (ALE) arising in the innermost iteration during the application of Rosenbrock ODE solvers to RDEs. We show that the LDLT‐type decomposition avoids complex arithmetic, as well as cancellation effects arising from indefinite right hand sides of the ALEs appearing in the classic ZZT based approach. Additionally, a certain number of linear system solves can be saved within the ADI algorithm by reducing the number of column blocks in the right hand sides while the full accuracy of the standard low‐rank ADI is preserved. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A geometrical numerical linear algebra approach to residual‐enhanced parametric model reduction
Authors: Zimmermann Ralf 
Published: December 2014

AbstractThe most prominent approaches to model reduction share the general principle, that a given large‐scale system is projected onto a suitable subspace spanned by a low‐dimensional basis. The projection basis essentially determines the approximation quality of the resulting reduced order system. Nonlinear parametric dependencies may be taken into account by applying interpolation techniques on matrix manifolds for computing projection bases and/or reduced systems at arbitrary parameter conditions, see [1] for a recent survey. In this short note, an original approach to enhance the prediction capabilities of the interpolated reduced‐order projection bases for parametrized linear systems is proposed. To this end, a suitable residual‐based goal function is introduced, which measures the approximation quality of a given projection subspace. As this function is invariant under changes of basis, it is to be considered as a mapping on the Grassmann‐Manifold Gr(n, p) of p‐dimensional subspaces of ℝn. As such, it may be optimized using the conjugate gradient method specifically adapted to the manifold structure of the Grassmannian Gr(n, p), [2,3]. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Wavelet compression of integral operators arising from boudary‐domain integral method
Authors: Ravnik Jure , Škerget Leopold 
Published: December 2014

AbstractThe boundary‐domain integral method uses Green's functions to write integral representations of partial differential equations. Since Green's functions are non‐local, the systems of linear equations arising from the discretization of integral representations are fully populated. Several algorithms have been proposed, which yield a data‐sparse approximation of these systems, such as the fast multipole method, adaptive cross approximation and among others, wavelet compression.In the framework of solving the Navier‐Stokes equations in velocity‐vorticity form one may utilize the boundary‐domain integral method for the solution of the kinematics equation to calculate the boundary vorticity values. Since the kinematics equation is a Poisson type equation, usually its integral representation is written with the Green's function for the Laplace operator. In this work, we introduce a false time into the equation and parabolize its nature. Thus, a time‐dependent Green's function may be used. This provides a new parameter, the time step, which can be set to control the Green's function. The time‐dependent Green's function is a global function, but by carefully choosing the time step, its behaviour is almost local. This makes it a good candidate for wavelet compression, yielding much better compression ratios at a given accuracy than when using the Green's function for the Laplace operator. However, as false time is introduced, several time steps must be solved in order to reach a converged solution. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Estimates of modeling errors for linear elliptic problems
Authors: Samrowski Tatiana S. 
Published: December 2014

AbstractWe derive new estimates of modeling errors for linear elliptic boundary value problems with periodic coefficients solved by homogenization method. Our approach is based on the concept of functional a posteriori error estimation. The estimates are obtained for the energy norm and use solely the global flux of the non‐oscillatory solution of the homogenized model and solution of a boundary value problem on the cell of periodicity. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Higher order Galerkin methods in time for free surface flows
Authors: Weller Stephan 
Published: December 2014

AbstractIn many engineering applications, free surface or two‐phase flows are discretized in time with an explicit decoupling of geometry and fluid flow. Such a strategy leads to a capillary CFL condition of the form
$\Delta t \le \sqrt{\rm{We}}\,h^{3/2}$
[3]. For the case of surface tension dominated flows (i.e. high Weber number We) this can dictate infeasibly small time steps.As an alternative we suggest a Galerkin method in time based on the discontinuous Galerkin method of first order (dG(1)). For this choice, an energy estimate can be proved [7], so unconditional stability of the method is given. While for ODEs or parabolic PDEs the method is of third order at the discrete points in time tn [4], in the case of free surface flows second order convergence can still be achieved.Numerical examples using the Arbitrary Lagrangian Eulerian (ALE) method for both capillary one‐phase and two‐phase flow demonstrate this convergence order. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Modelling and Simulation of the Transport of Protein Foams
Authors: Gladbach Katharina , Delgado Antonio , Rauh Cornelia 
Published: December 2014

AbstractThe behaviour of foams at rest, but particularly during fluid mechanical transport is not sufficiently investigated yet. The present article deals with protein foams as they have a great importance in food production. In the first part, the foaming process of a highly viscous liquid due to gaseous materials dispersed under pressure in the liquid and mass transport of volatile components dissolved in the liquid is considered. The aim is to calculate the foam volume and the concentration of the dissolved, volatile components as a function of the material and process parameters. In the second part, material equations for bubble suspensions with gas volume fractions ϕ ≤ 0.6 and small bubble deformations (i.e. NCa ≪ 1) are presented. The basics form two constitutive laws which are used for describing a steady shear flow. If the rates of work of the two models are compared, material equations for the shear viscosity and the normal stress differences can be derived. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Spectral Bounds on the Solution of Linear Time‐Periodic Systems
Authors: Benner Peter , Denißen Jonas 
Published: December 2014

AbstractLinear time‐periodic systems arise whenever a nonlinear system is linearized about a periodic trajectory. Stability of the solution may be proven by rigorous bounds on the solution. The key idea of this paper is to derive Chebyshev projection bounds on the original system by solving an approximated system. Depending on the smoothness of the original function, we formulate two upper bounds. The theoretical results are illustrated and compared to trigonometric spline bounds by means of two examples which include an anisotropic rotor‐bearing system. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Sensitivities for topological graph changes in finite element meshes and application to adaptive refinement
Authors: Friederich Jan , Leugering Günter , Steinmann Paul 
Published: December 2014

AbstractWe propose a novel approach to adaptivity in FEM based on local sensitivities for topological mesh changes. To this end, we consider refinement as a continuous operation on the edge graph of the finite element discretization, for instance by splitting nodes along edges and expanding edges to elements. Thereby, we introduce the concept of a topological mesh derivative for a given objective function that depends on the discrete solution of the underlying PDE. These sensitivities may in turn be used as refinement indicators within an adaptive algorithm. For their calculation, we rely on the first‐order asymptotic expansion of the Galerkin solution with respect to the topological mesh change. As a proof of concept, we consider the total potential energy of a linear symmetric second‐order elliptic PDE, minimization of which is known to decrease the approximation error in the energy norm. In this case, our approach yields local sensitivities that are closely related to the reduction of the energy error upon refinement and may therefore be used as refinement indicators in an adaptive algorithm. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Optimal Control of an Elastic Tyre‐Damper System with Road Contact
Authors: Kimmerle Sven‐Joachim , Moritz Roman 
Published: December 2014

AbstractWe study an elastic tyre with a wheel rim that is suspended at the chassis of a car by means of a spring‐damper element. This quarter car model may be controlled by varying the damping constant of the electrorheological damper. Our mathematical model yields a coupled ODE‐PDE problem with a free boundary at the tyre‐road contact. In this study we approximate the tyre by the Hertz contact stress formula. The resulting optimal control problem with control constraints is solved numerically. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Pole placement by dynamic output feedback of minimal order
Authors: Franke Matthias , Röbenack Klaus 
Published: December 2014

AbstractIn the present contribution, an approach for calculating a dynamic output feedback of minimal order is presented. The feedback is of minimal order in the sense that the controller state has lowest possible dimension among all controllers placing the poles of the closed loop system as desired. The main idea is to extend the system under consideration succesively by independent integrators until a static compensator can be computed. This is also discussed on a computational example. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Dynamical Modeling and Flatness Based Control of a Belt Drive System
Authors: Jörgl Matthias , Gattringer Hubert 
Published: December 2014

AbstractBelt driven systems are part of many industrial applications, like computerized numerical control (CNC) machines in particular cutting machines and 3D‐printers. In this paper the dynamical modeling and a flatness based controller design for belt driven systems are proposed. Due to the special kinematics, the stiffness of the belt is nonlinear, leading to nonlinear equations of motion. By neglecting some minor dynamical effects, the resulting system simplifies to a differentially flat one. This allows to calculate nominal feed‐forward control torques by using the flat output of the system. To stabilize the error dynamics, an additional PD control law is introduced. The proposed method is compared with a controller, where elastic deflections for the feed forward part are neglected and elastic deformations are compensated by modifying the desired trajectories in a model‐based manner. The tracking performance of both methods is evaluated in certain simulations and experiments. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Modeling, simulation and adaptive process control of biotechnological processes in decentralized anaerobic treatment of domestic wastewater
Authors: Vega‐De Lille Marisela , Groß Frauke , Delgado Antonio 
Published: December 2014

AbstractControl in anaerobic wastewater treatment plants is difficult to achieve but necessary due to a high sensitivity to disturbances and process complexity. With the help of different mathematical tools, control strategies can be developed. Particularly, a well‐defined mathematical model can be highly effective for design, assessment and optimization of treatment plants. However, applications directly in the control system of a treatment plant are hard to achieve due to model complexity and usually require specialized software and the engagement of experts in the subject. The objective of the present study was the development of less empirical methods for assessment and control of a decentralized anaerobic plant for the treatment of domestic wastewater. A lab‐scale plant, which consisted of a two‐stage anaerobic digestion process followed by an anaerobic ammonium oxidation (ANAMMOX) reactor for nitrogen removal, was used as object of study. Ordinary differential equation models were implemented to simulate the processes that took place in the treatment plant. With the help of the implemented models, control tools were developed. These tools include a standalone application for monitoring of the two‐stage anaerobic digestion process and an ammonium estimator for the ANAMMOX reactor by means of artificial neural networks (ANNs). The procedures followed aimed to reduce the amount of experimental work required so they can be easily transferred from laboratory to full‐scale conditions. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Variational approach to modeling and control of dynamic systems with distributed parameters
Authors: Kostin Georgy 
Published: December 2014

AbstractControlled motions of a thin elastic rod are studied. A variational statement of the initial‐boundary value problem is given based on the integral formulation of constitutive relations. An approach relying on the Ritz method and finite element technique is proposed to design the boundary control that moves the rod with certain accuracy to a given final state and minimizes the mean energy. The results of numerical simulation and the estimates of solution quality are presented and discussed. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Feedback control for parabolic systems with in‐domain actuation
Authors: Wang Siqian , Woittennek Frank , Knüppel Torsten 
Published: December 2014

AbstractState feedback design for linear parabolic systems with in‐domain actuation and general Robin boundary conditions is considered. To this end the system is shown to be state equivalent to a boundary controlled system. By means of the backstepping transformation the latter system is shown to be feedback equivalent to a stable parabolic equation. Within the contribution previous results concerning such systems are supplemented by numerical simulation studies. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Normal form observers for hyperbolic distributed parameter systems with spatially varying coefficients
Authors: Woittennek Frank 
Published: December 2014

AbstractObserver design for 1D linear distributed parameter systems of hyperbolic type with boundary measurement is discussed. The approach is based on the observer canonical form introduced on the basis of a functional‐differential equation (f.d.e.) equivalent to the original posed boundary value problem. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Constraint handling in optimization‐based control of a heat‐up problem using a transformation approach
Authors: Utz Tilman , Rhein Sönke , Graichen Knut 
Published: December 2014

AbstractAn approach is presented for optimization‐based control of a class of boundary‐controlled parabolic partial differential equations, which are subject to state and input constraints. In order to avoid the potential numerical complexity of constrained optimization, suitably chosen asymptotic saturation functions are used to reformulate the original problem in new coordinates. The resulting unconstrained problem can then be solved with methods of unconstrained optimization, which is interesting for use in model predictive control schemes. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Nonlinear MPC: the Impact of Sampling on Closed Loop Stability
Authors: Worthmann Karl , Reble Marcus , Grüne Lars , Allgöwer Frank 
Published: December 2014

AbstractIn this paper we consider model predictive control (MPC) schemes without stabilizing terminal constraints and/or costs for continuous time systems. While the estimates on the required prediction horizon length such that asymptotic stability of the MPC closed loop is guaranteed yield, in general, satisfactory results their applicability is limited due to the fact that the respective proofs assume that the input function can be switched arbitrarily often on compact time intervals. We present a technique which allows to determine a suitable discretization accuracy such that the obtained performance bound is preserved while the control signal is only switched at the sampling instants of the corresponding sampled data system. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A Hybrid Systems Framework for Motion Planning with Motion Primitives of Mechanical Systems
Authors: Flaßkamp Kathrin , Hage‐Packhäuser Sebastian , Ober‐Blöbaum Sina 
Published: December 2014

AbstractMotion planning with motion primitives is a solution concept for the optimal control of mechanical systems based on a quantization of the search space. In this contribution, we write the resulting system as a hybrid automaton and discuss the arising structures. In this context, we focus on the exploitation of symmetries. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)