Bernhard Bachmann
Bielefeld University of Applied Sciences
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Featured researches published by Bernhard Bachmann.
international modelica conference | 2011
Willi Braun; Lennart Ochel; Bernhard Bachmann
Jacobian matrices are used in a wide range of applications - from solving the original DAEs to sensitivity analysis. Using Automatic Dierentiation the necessary partial derivatives can be provided eciently within a Modelica-Tool. This paper describes the corresponding implementation work within the OpenModelica Compiler (OMC) to create a symbolic derivative module. This new OMC-feature generates symbolically partial derivatives in order to calculate Jacobian matrices with respect to dierent variables. Applications
Journal of Integrative Bioinformatics | 2011
Sabrina Pross; Bernhard Bachmann
Biological systems are often very complex so that an appropriate formalism is needed for modeling their behavior. Hybrid Petri Nets, consisting of time-discrete Petri Net elements as well as continuous ones, have proven to be ideal for this task. Therefore, a new Petri Net library was implemented based on the object-oriented modeling language Modelica which allows the modeling of discrete, stochastic and continuous Petri Net elements by differential, algebraic and discrete equations. An appropriate Modelica-tool performs the hybrid simulation with discrete events and the solution of continuous differential equations. A special sub-library contains so-called wrappers for specific reactions to simplify the modeling process. The Modelica-models can be connected to Simulink-models for parameter optimization, sensitivity analysis and stochastic simulation in Matlab. The present paper illustrates the implementation of the Petri Net component models, their usage within the modeling process and the coupling between the Modelica-tool Dymola and Matlab/Simulink. The application is demonstrated by modeling the metabolism of Chinese Hamster Ovary Cells.
IFAC Proceedings Volumes | 2013
Alachew Shitahun; Vitalij Ruge; Mahder Gebremedhin; Bernhard Bachmann; Lars Eriksson; Joel Andersson; Moritz Diehl; Peter Fritzson
This paper demonstrates model-based dynamic optimization through the coupling of two open source tools: OpenModelica, which is a Modelica-based modeling and simulation platform, and CasADi, a framework for numerical optimization. The coupling uses a standardized XML format for exchange of differential-algebraic equations (DAE) models. OpenModelica supports export of models written in Modelica and the optimization language extension using this XML format, while CasADi supports import of models represented in this format. This allows users to define optimal control problems (OCP) using Modelica and optimization language specification, and solve the underlying model formulation using a range of optimization methods, including direct collocation and direct multiple shooting. The proposed solution has been tested on several industrially relevant optimal control problems, including a diesel-electric power train.
equation based object oriented modeling languages and tools | 2014
Patrick Täuber; Lennart Ochel; Willi Braun; Bernhard Bachmann
This paper is concerned with the tearing method according to François Cellier. Tearing is used to reduce the dimension of algebraic loops, which inevitably arise in the modelling of scientific systems using differential-algebraic equations, as far as possible to achieve an efficient simulation. However, the original tearing method according to Cellier is not suitable for the application in practice, since restrictions on the solvability of equations for variables, and other features, which appear in reality, are not considered. In this work, different changes to the method are introduced and tested, which make it possible to use Cellier Tearing in practice. In addition, the modeller can influence the selection of tearing variables. Modifications of the integrated heuristic are presented, whose efficiency is statistically evaluated at the end of this work. With these changes and the new heuristics, Celliers method becomes a very suitable way to optimize the efficiency of simulation in practice.
Applied Mathematics and Computation | 2016
Xiaolin Qin; Juan Tang; Yong Feng; Bernhard Bachmann; Peter Fritzson
In many mathematical models of physical phenomenons and engineering fields, such as electrical circuits or mechanical multibody systems, which generate the differential algebraic equations (DAEs) systems naturally. In general, the feature of DAEs is a sparse large scale system of fully nonlinear and high index. To make use of its sparsity, this paper provides a simple and efficient algorithm for index reduction of large scale DAEs system. We exploit the shortest augmenting path algorithm for finding maximum value transversal (MVT) as well as block triangular forms (BTFs). We also present the extended signature matrix method with the block fixed point iteration and its complexity results. Furthermore, a range of nontrivial problems are demonstrated by our algorithm.
Information Technology | 2014
Sabrina Proß; Bernhard Bachmann
Abstract A Petri net library, called PNlib, is presented to enable graphical hierarchical modeling, hybrid simulation and animation of processes in life sciences among others. In order to model these processes, a powerful and universally usable mathematical modeling concept – xHPN (extended Hybrid Petri Nets) – has been established. This formalism is used as specification for the PNlib realized by the object-oriented modeling language Modelica. The PNlib is freely available and can be downloaded on the Modelica homepage www.modelica.org/libraries.
IFAC Proceedings Volumes | 2012
Sabrina Proß; Bernhard Bachmann
Abstract An environment has been developed which comprises mathematical methods, concepts, and tools to enable the processing of experimental data to usable new insights about biological systems. Therefore, a mathematical modelling concept - Hybrid Petri-Nets for biological applications (HPNbio) – has been defined which is properly adapted to the demands of biological process. This concept has been implemented with the object-oriented modelling language Modelica. The developed Modelica library, called PNlib (Petri Net library), in combination with an appropriate Modelica-tool enables graphical hierarchical modelling, hybrid simulation, and animation of HPNbio-models. Thereby, an additional Modelica library, called PNproBio (Petri Nets for process modelling of Biological systems), provides wrapped HPNbio which offers on the one hand an easy-use-model at the top level with an intuitive and familiar adapted biological view and on the other hand the flexibility and generality of the HPNbio concept at a lower level. Based on an established model, the underlying processes can be optimized. This process optimization procedure is performed by means of hybrid optimization methods, i.e. a global method is combined with a local method by use of a specific switching strategy, in order to realize an open-loop control for biological processes.
Applied Mathematics and Computation | 2018
Xiaolin Qin; Lu Yang; Yong Feng; Bernhard Bachmann; Peter Fritzson
High index differential algebraic equations (DAEs) are ordinary differential equations (ODEs) with constraints and arise frequently from many mathematical models of physical phenomenons and engineering fields. In this paper, we generalize the idea of differential elimination with Dixon resultant to polynomially nonlinear DAEs. We propose a new algorithm for index reduction of DAEs and establish the notion of differential Dixon resultant, which can provide the differential resultant of the enlarged system of original equations. To make use of structure of DAEs, variable pencil technique is given to determine the termination of differentiation. Moreover, we also provide a heuristic method for removing the extraneous factors from differential resultant. The experimentation shows that the proposed algorithm outperforms existing ones for many examples taken from the literature.
equation based object oriented modeling languages and tools | 2016
Patrick Täuber; Lennart Ochel; Bernhard Bachmann
Common tearing methods try to find static tearing variables. This means that selected tearing variables are used for the entire simulation, which also means that all inner equations are used for the entire simulation. Hence, the tearing method sets up the tearing system in a way, that there are no restrictions on the domain of the inner equations. In general, this leads to bigger tearing sets. This paper presents an extension of common tearing methods that generates another tearing set in addition. The additional set has fewer tearing variables, which means that it should be more efficient in general. However, the additional set has some restrictions on its domain of definition. That is why common approaches would not even create it and why it may not be used for the entire simulation. Hence, its domain needs to be analysed during simulation to validate if the smaller set is defined on the current domain. If that is the case the smaller set is used for the calculation, otherwise the original set is used. This paper shows how this additional tearing set can be generated. It is also demonstrated how the domain can be monitored during runtime in order to make the switching process efficient. Results using a prototype implementation in OpenModelica are analysed to show the benefits of this method.
international modelica conference | 2012
Bernhard Bachmann; Lennart Ochel; Vitalij Ruge; Mahder Gebremedhin; Peter Fritzson; Vaheed Nezhadali; Lars Eriksson; Martin Sivertsson