Auer Ekaterina

• University of Duisburg-Essen

Interval methods are helpful in the context of scientific computing for reliable treatment of problems with bounded uncertainty. Most traditional interval algorithms, however, were designed for sequential execution while internally depending on processor-specific instructions for directed rounding. Nowadays, many-core processors and dedicated hardw...

In this paper, we describe the requirements for traceable open-source data retrieval in the context of computation of BRCA1/2 mutation probabilities (mutations in two tumor-suppressor genes responsible for hereditary BReast or/and ovarian CAncer). We show how such data can be used to develop a Dempster-Shafer model for computing the probability of...

In various research projects, it has been demonstrated that feedforward neural network models (possibly extended toward dynamic representations) are efficient means for identifying numerous dependencies of the electrochemical behavior of high-temperature fuel cells. These dependencies include external inputs such as gas mass flows, gas inlet temper...

Many dynamic system models in population dynamics, physics and control involve temporally delayed state information in such a way that the evolution of future state trajectories depends not only on the current state as the initial condition but also on some previous state. In technical systems, such phenomena result, for example, from mass transpor...

The dynamic operation of high-temperature fuel cells under temporally varying electric loads requires models for the electric stack power that depend on the supplied fuel mass flow, the electric current, the temperature of the supplied reaction media, and the stack temperature. This information is required to optimize the fuel consumption when trac...

The dynamic operation of high-temperature fuel cells under temporally varying electric loads requires models for the electric stack power that depend on the supplied fuel mass flow, the electric current, the temperature of the supplied reaction media, and the stack temperature. This information is required to optimize the fuel consumption when trac...

The dynamic operation of high-temperature fuel cells under temporally varying electric loads requires models for the electric stack power that depend on the supplied fuel mass flow, the electric current, the temperature of the supplied reaction media, and the stack temperature. This information is required to optimize the fuel consumption when trac...

Methods with result verification, for example, interval analysis, have been applied in engineering since the 1970s at the latest. They help not only to prove automatically that computer-obtained results are correct, but also to represent bounded uncertainty and propagate it through system models in an easy-to-understand, deterministic manner. After...

Zusammenfassung Bei einer Vielzahl von Anwendungen aus dem Bereich der Ingenieurwissenschaften ist die Berechnung garantierter Einschlüsse der Mengen aller erreichbaren Zustandsgrößen von großem Interesse. Mögliche Anwendungsszenarien umfassen den Entwurf sowie die rechnergestützte Verifikation von (nicht-)linearen Zustandsregelungen sowie die Impl...

Various evaluation approaches exist for multi-purpose visual analytics (VA) frameworks. They are based on empirical studies in information visualization or on community activities, for example, VA Science and Technology Challenge (2006-2014) created as a community evaluation resource to 'decide upon the right metrics to use, and the appropriate imp...

In this paper, we describe how to enhance experimental parameter identification for cooperative systems using the GPU. This kind of identification is necessary, for example, in the area of developing robust controllers and observers based on available measurement data. First, we point out which parts of the general, global optimization based parame...

In this paper, we take a look at the analysis and parameter identification for control-oriented, dynamic models for the thermal subsystem of solid oxide fuel cells (SOFC) from the systematized point of view of verification and validation (V&V). First, we give a possible classification of models according to their verification degree which depends,...

In this paper, we implement a simple verified ODE solver to run on the GPU as a first step towards GPU-based fully verified parameter identification. Our goal is to use the proposed parallelization to speed up parameter identification for dynamic SOFC models based on ordinary differential equations. We illustrate the potential of the approach using...

The computation of guaranteed state enclosures has a large variety of applications in engineering if initial value problems for sets of ordinary differential equations are concerned. One possible scenario is the use of such state enclosures in the design and verification of linear and nonlinear feedback controllers as well as in predictive control...

The importance of the Dempster-Shafer theory (DST) for modeling and propagating uncertainty has grown in the recent past. An obstacle for wider application of this theory in industrial practice is the lack of software support for analysts. The few tools available depend on floating point arithmetic and do not consider the inherently interval-based...

In this paper, we introduce simplified models for the thermal subsystem of solid oxide fuel cells, which are considered to consist of two preheaters and one finite volume element to describe the temperature of the stack. The simplifying assumption, which allows us to obtain analytical solutions to the underlying system of differential equations, is...

Reliable control strategies for complex dynamic systems have to account for stability and robustness despite the presence of both parameter uncertainty and measurement errors. In addition, such control strategies have to comply with performance specifications that can be described either by the minimization of suitable cost functions or by direct s...

The technology of solid oxide fuel cells is one of the important topics in modern engineering. One research direction is to design robust and accurate control strategies for this kind of fuel cells based on models spatially discretized into ordinary differential equations. To allow users to employ new models and techniques easily in combination wit...

In many applications, there is a need to choose mathematical models that depend on non-smooth functions. The task of simulation becomes especially difficult if such functions appear on the right-hand side of an initial value problem. Moreover, solution processes from usual numerics are sensitive to roundoff errors so that verified analysis might be...

In this paper, we discuss parameter identification for models based on ordinary differential equations in the context of solid oxide fuel cells. In this case, verified methods (e.g. interval analysis), which provide a guarantee of correctness for the computed result, can be of great help for dealing with the appearing uncertainty and for devising a...

Markov chains provide quite attractive features for simulating a system’s behavior under consideration of uncertainties. However, their use is somewhat limited because of their deterministic transition matrices. Vague probabilistic information and imprecision appear in the modeling of real-life systems, thus causing difficulties in the pure probabi...

In this contribution, we present interval methods for mathematical modeling, for parameter identification, and for control design of dynamical systems. The corresponding approaches are applied to the thermal subsystem of a high-temperature solid oxide fuel cell (SOFC) which is available as a test rig at the Chair of Mechatronics at the University o...

Solid oxide fuel cells (SOFCs) can be used as decentralized energy supply devices for providing electricity and heat directly by converting chemical energy. In such applications of SOFCs, the electric power demand is commonly varying over time. Therefore, all processes in fuel cell systems are typically instationary. For example, the heating and co...

Fault tree analysis is a method to determine the likelihood of a system attaining an undesirable state based on the information about its lower level parts. However, conventional approaches cannot process imprecise or incomplete data. There are a number of ways to solve this problem. In this paper, we will consider the one that is based on the Demp...

In many control applications, we are interested in accurate trajectory tracking. This is especially true for cases in which exact analytic solutions are not available because initial states are not consistent with the desired state or output trajectories or because parameters are significantly uncertain. In these cases, control strategies can be de...

For nonlinear systems, feedback control strategies have to be parameterized in such a way that they guarantee asymptotic stability in a certain neighborhood of desired operating points or desired trajectories. Due to not exactly known initial conditions, parameter uncertainties, and measurement errors characterizing dynamic system models in real ap...

Obtaining verified numerical solutions to initial value problems (IVPs) for ordinary differential equations (ODEs) is important in many application areas (e.g. biomechanics or automatic control). During the last decades, a number of solvers have been developed for this purpose. However, they are rarely used by industry engineers. One reason for thi...

ValEncIA-IVP is a verified solver for initial value problems for sets of ordinary differential equations which determines guaranteed enclosures of all reachable states. In this paper, we present its new features which allow for a wider application domain. They also improve the performance of ValEncIA-IVP. Especially for the simulation of asymptotic...

In many applications in control engineering, accurate feedforward control strategies have to be developed which aim at tracking of desired state or output trajectories. For differentially flat dynamic systems, this task is usually solved analytically by symbolic formula manipulation which is supported by software tools like MAPLE. However, these an...

The stabilization of stance is a subject of continuing research in biology, biomechanics and robotics. It plays an important role in many clinical applications as well as in forward dynamical gait simulation. In this paper, we propose a new model relying on a two cylinder foot contact scheme. This contact model has the advantage of simple and smoot...

Interval numerical methods produce results that can have the power of a mathematical proof. Although there is a substantial amount of theoretical work on these methods, little has been done to ensure that an implementation of an interval method can be readily verified. However, when claiming rigorous numerical results, it is crucial to ensure that...

Solving initial value problems (IVPs) for ordinary differential equations (ODEs) is a common task in many scientific fields. Over the last decades, several different verified techniques have been developed to compute enclosures of the exact result numerically. The obtained bounds are guaranteed to contain the corresponding solution to the IVP and c...

During the last decades, computer assisted modeling and analysis of different industrial processes have increased in importance. Computers help to reduce the design and development time for new products and to substitute low cost virtual tests for expensive experiments on real life prototypes. However, the results are often unreliable due to errors...

The importance of the Dempster-Shafer theory (DST) for modeling and propagating uncertainty has grown in the recent past. An obstacle for wider application of this theory in industrial practice is the lack of software support for analysts. The few tools available depend on floating point arithmetic and do not consider the inherently interval-based...

In recent years, powerful interval arithmetic tools have been developed for the computation of guaranteed enclosures of the sets of all reachable states for dynamical systems. In such simulations, uncer-tainties in initial conditions and parameters are considered in terms of intervals which contain their complete possible range. The resulting en-cl...

Solving initial value problems for ordinary differential equations is a common task in many disciplines. Over the last decades, several different verified techniques have been developed to compute enclosures of the exact result numerically. The obtained bounds are guaranteed to contain the corresponding solution to the initial value problem. Ideall...

Uses of New Sensitivity and Dae Solving Methods in SmartMobile for Verified Analysis of Mechanical Systems Software for modeling and simulation (MSS) of mechanical systems helps to reduce production costs for industry. Usually, such software relies on (possibly erroneous) finite precision arithmetic and does not take into account uncertainty in the...

The influence of bounded uncertainties in parameters and initial conditions of dynamical systems can be analyzed efficiently with the help of interval methods. In engineering, interval arithmetic tools are usually applied offline to verify, analyze, and design dynamical systems. In this contribution, we describe interval-based techniques for online...

In this contribution, we present three selected applications of verified DAE solvers in engineering. The applications under consideration are • simulation of sets of differential algebraic equations (DAEs) including computation of enclosures of consistent initial conditions, • computation of feedforward control sequences in such a way that the sy...

To automatize modeling and simulation of mechanical systems for industry and research, a number of tools were developed, among which the program MOBILE plays a considerable role. However, such tools cannot guarantee the correctness of results, for example, because of possible errors in the underlying finite precision arithmetic. To avoid such error...

In this paper, ValEncIA-IVP, a novel approach for VALidation of state ENClosures using Interval Arithmetic for Initial Value Problems, is presented to determine guaranteed state enclosures. The algorithm is based on the computation of non-validated approximate solutions followed by an interval arithmetic fixed-point iteration for enclosing the appr...

Computer simulations of real life processes can generate erroneous results, in many cases due to the use of finite precision arithmetic. To ensure correctness of the results obtained with the help of a computer, various kinds of validating arithmetic and algorithms were developed. Their purpose is to provide bounds in which the exact result is guar...

In this paper, we introduce a general-purpose approach for the detec-tion and reduction of overestimation in verified interval simulations of the dynamics of mechanical systems. For that purpose, we automatically de-rive constraints which eliminate physically meaningless parts of the state enclosures of the corresponding ordinary differential equat...

In this paper, we present several aspects of the recent project PROREOP, in which a new prognosis system is developed for optimizing patient-specific preoperative surgical planning for the human skeletal system. We address verification and validation assessment in PROREOP with special emphasis on numerical accuracy and performance. To assess numeri...

Simulation techniques are commonly used to analyze the influence of uncertainties of initial conditions and systemparameters on the trajectories of the state variables of dynamical systems. In this context, interval arithmetic approaches are of interest. They are capable of determining guaranteed bounds of all reachable states if worst‐case bounds...

In this paper, we present an integrated environment for validated modeling and simulation of kinematics and dynamics of various classes of mechanical systems SMARTMOBILE (Simulation and Modeling of dynAmics in MOBILE: Reliable and Template–based) built on top of the non-validated tool MOBILE. We outline the main features of SMARTMOBILE and its appl...

Multibody modeling and simulation is important in many areas of our life from a computer game to space exploration. To automatize the process for industry and research, a lot of tools were developed, among which the program MOBILE plays a considerable role. However, such tools cannot guarantee the correctness of results, for example, due to possibl...

In this contribution, a detailed comparison of different validated solvers for initial value problems for ordinary differential equations (ODEs) is presented. The performance of the interval arithmetic solver ValEncIA-IVP (VALidation of state ENClosures using I nterval Arithmetic for Initial Value Problems, http://www.valencia-ivp.com), which has b...

In this note we discuss strategies that would enhance modern modeling and simulation software (MSS) with reliable routines using validated data types, controlled rounding, algorithmic differentiation and interval equation or initial value problem solver. Several target systems are highlighted. In stochastic traffic modeling, the computation of work...

We will show how a variety of interval algorithms have found their use in the multibody modeling program MOBILE. This paper ac- quaints the reader with the key features of this open source software, describes how interval arithmetic help to implement new transmission elements, and reports on interval modeling of dynamics, which is an inherent part...