Benchmarks for Hybrid Modelling

Hybrid Modelling is getting more and more important in technical and natural sciences. In these fields very complex systems and processes have to be simulated and therefore proper models must be developed. For complex systems different model structures for dynamical systems are available. One of the important model structures regarding complex dynamical systems are hybrid models. A hybrid model consists of several dynamical models and a state diagram where each state is described by a differential algebraic equation (DAE). This paper deals with benchmarks out of different fields of applications of this modelling approach. The first benchmark is an electrical circuit with linear devices and a diode as a nonlinear component. This example will show the influence of a simple model to the state space description or the corresponding differential algebraic description. The different models for the nonlinear behaviour of the diode influences the states of the state diagram. It is remarkable, that the different models for the diode results in a different hybrid model. The influence from these models on the diode can be observed. Another benchmark is the rotating pendulum. It is also described by a state diagram, in this special academic example a state diagram with two states. The two examples are representative, one out of the field of electrical engineering, one typical mechanical scenario. In the article two aspects will be considered. On the one side the modelling process of the electrical circuit will be observed in detail, especial the influence of different diode models on the structure of the states, and the state transition between the two states of the mechanical pendulum. On the other side also the need of a mathematical notation and description of the states and their transition will be discussed. In the end of the article some comments to the simulation of hybrid systems will be given

Microsimulation Models for Simulating Pathways of Patients with Mental Diseases

Predicting demand for care is necessary to provide sufficient capacities in hospitals and enable better planning to cope with challenges like changes in the structure of the population. Emphasis in this work is put on the analysis of the data and on the parametrization of a simulation model for the paths of patients with mental diseases through the health care system. Survival analysis and model selection methods are used for this purpose. Data on patients and their treatments is analyzed with methods of survival analysis. Different methods for modelling the survival and hazard function are presented and compared. Hereby, the focus is on the cox model. It is used to model the hazard function and can be extended to analyze multiple events. With the use of model selection methods the significant parameters are determined. Only these are included in the simulation model. These methods shall help to raise the quality of the parametrization and therefore the whole simulation model. In the microsimulation model, every patient has a particular set of parameters and can be in one of several predefined, exclusive states. The events are implemented as state changes. The probabilities for the events are calculated using the hazard functions. These are estimated with several extensions of the cox model. The considered events in the simulation are readmissions to hospital and contacts to ambulant psychiatrists. The simulation runs for a predefined time span and the sequence of events of each patient is tracked. After the simulation, the individual paths of the patients as well as aggregated quantities such as the overall numbers of certain events are analyzed. Simulations for different populations are performed. The results for various scenarios are presented. Scenarios with and without contacts to a psychiatrist are considered as well as different maximum numbers of admissions. Also, the subpopulations are compared. For example, differences in the results for diagnosis groups are encountered. These simulations shall lead to an improvement of the prediction of the pathways of the patients and therefore help to evaluate interventions like treatment changes the health care system or the utilization of the capacities in hospitals

Microsimulation Models for Simulating Pathways of Patients with Mental Diseases

Predicting demand for care is necessary to provide sufficient capacities in hospitals and enable better planning to cope with challenges like changes in the structure of the population. Emphasis in this work is put on the analysis of the data and on the parametrization of a simulation model for the paths of patients with mental diseases through the health care system. Survival analysis and model selection methods are used for this purpose. Data on patients and their treatments is analyzed with methods of survival analysis. Different methods for modelling the survival and hazard function are presented and compared. Hereby, the focus is on the cox model. It is used to model the hazard function and can be extended to analyze multiple events. With the use of model selection methods the significant parameters are determined. Only these are included in the simulation model. These methods shall help to raise the quality of the parametrization and therefore the whole simulation model. In the microsimulation model, every patient has a particular set of parameters and can be in one of several predefined, exclusive states. The events are implemented as state changes. The probabilities for the events are calculated using the hazard functions. These are estimated with several extensions of the cox model. The considered events in the simulation are readmissions to hospital and contacts to ambulant psychiatrists. The simulation runs for a predefined time span and the sequence of events of each patient is tracked. After the simulation, the individual paths of the patients as well as aggregated quantities such as the overall numbers of certain events are analyzed. Simulations for different populations are performed. The results for various scenarios are presented. Scenarios with and without contacts to a psychiatrist are considered as well as different maximum numbers of admissions. Also, the subpopulations are compared. For example, differences in the results for diagnosis groups are encountered. These simulations shall lead to an improvement of the prediction of the pathways of the patients and therefore help to evaluate interventions like treatment changes the health care system or the utilization of the capacities in hospitals

Logging of Data for EOG Signals in Ambient Assisted Living Controlled via Mobile Devices

The paper describes a portable device for recording eye movements through Electrooculography (EOG). The gained bio signal can be used for monitoring the vigilance or basic eye control commands. The measurement is done with sticky electrodes; therefore it is non-invasive and easy to use. A special dedicated hardware device was developed for the purpose of data acquisition. The device has been tailored to be used in real life environments. The device allows rechargeable battery powered data acquisition of 3 EOG channels with 24bit resolution and 250Hz sampling rate per channel, over a period of up to 10 hours. Time information is provided by a built -in real time clock. The collected data is pre-processed and can be stored on a memory card or streamed directly via Bluetooth using a serial port profile to a mobile device. The mobile application can be used for data post-processing as well as for the adjustment of measurement device settings

Testing and Assessment in Mathematics via Web Applications

This paper deals with the web interface Maple T.A. which is used for mathematical education at the Vienna University of Technology. Maple T.A. is based on the computer algebra system Maple. This fact offers the possibility to test and assess the students in easy but also complex mathematical matters in an uncomplicated way. This interface was first used only for the refresher course. This course takes place in the first 3 weeks of the semester and deals with the repetition of all the important themes of the school mathematics. Maple T.A. is also used for the basic and advanced mathematical courses in the first two years in the study of electrical engineering. For these courses the use of Maple T.A. includes the offer of assignments for every chapter of the lecture but also homework and tests are realized in it

A Web-based Platform for E-Learning and Blended Learning in Modelling and Simulation

The Mathematics Modelling and Tools (MMT) e-learning system is a platform used for supporting lectures and tutoring at the Vienna University and Technology. Additionally to traditional e-learning properties like up- and download of lecture notes, videos and slides the MMT system provides the surface for a virtual modelling and simulation laboratory. Very powerful calculation software like MATLAB, Java or Octave, running in behind, allows experimenting with targeted modelling and simulation examples prepared and developed by experts. These are first of all used to support the presentation directly at the lecture and can afterwards be accessed by students given a password at home. As especially MATLAB also allows development of suitable examples dealing with mathematics, so far about ten percent of all examples treat this specific topic and are used in math lectures. It showed that especially the live experience fiddling on pre-implemented examples poses a big improvement for lectures

A Web-based Platform for E-Learning and Blended Learning in Modelling and Simulation

The Mathematics Modelling and Tools (MMT) e-learning system is a platform used for supporting lectures and tutoring at the Vienna University and Technology. Additionally to traditional e-learning properties like up- and download of lecture notes, videos and slides the MMT system provides the surface for a virtual modelling and simulation laboratory. Very powerful calculation software like MATLAB, Java or Octave, running in behind, allows experimenting with targeted modelling and simulation examples prepared and developed by experts. These are first of all used to support the presentation directly at the lecture and can afterwards be accessed by students given a password at home. As especially MATLAB also allows development of suitable examples dealing with mathematics, so far about ten percent of all examples treat this specific topic and are used in math lectures. It showed that especially the live experience fiddling on pre-implemented examples poses a big improvement for lectures

More-Space – A Simulation Tool for University Room Management

As proposed in various studies, educational facilities hold a high potential yield for improvement of room utilization. The goal of the project “MoreSpace” at Vienna University of Technology (TU Vienna) was to develop a hybrid modeling approach which helps to increase the efficiency of the university’s space utilization. Besides coupling of Discrete Event Simulation (DEVS), Agent-based (AB) methods and Cellular Automata (CA), successful deployment of such a model requires a thorough integration within the peripheral system. Which in turn leads to preconditions that have to be met, (e.g. by input - data, visualization of results, dissemination, etc.). This paper covers the methods applied for analyses of the model and the peripheral system, which enable model integration. For this is necessary to also focus on the psycho-social layer of the institution, as it is this layer that often leads to rejection of otherwise “good” solutions by the people within institutions. The paper further describes a deployment matrix which puts the simulations - models mode of operation (i.e. one time utilization for consulting, recurrent and frequent utilization) into context with met preconditions and the required depth of system integration. This allows it to estimate whether a model can be deployed as intended or not; with alternatives being either a transformation of the system, reformulation of the question(s) towards the model or - in the worst case - abortion of the deployment process. In the latter case the value of the deployment matrix lies within an early judgment of the situation saving resources that would have been spend otherwise. In addition it is possible to use these for developing alternative solutions in support of the intentional goals

Erlangen von Verständnis und Erlernen von Fertigkeiten in der Mathematik einmal anders

Der folgende Artikel behandelt die Vorstellung eines didaktischen Konzepts sowie deren Umsetzung und Auswirkungen in den Lehrveranstaltungen Mathematik für Elektrotechnik an der Technischen Universität Wien. Im ersten Abschnitt wird die Struktur der Lehrveranstaltungen vor den Projektmaßnahmen beschrieben. Dabei werden Defizite der alten Struktur aufgezeigt und die durch das Projekt initiierten Änderungen in Vorlesungen und Übungen vorgestellt. Deren praktische Umsetzung beschreibt der darauffolgende Abschnitt. Die Ergebnisse der im Anfangsstadium befindlichen Evaluation werden präsentiert und diskutiert. Weiterführende Transferüberlegungen werden im letzten Teil erörtert. 10.11.2014 | Andreas Körner, Stefanie Winkler, Carina Pöll & Felix Breitenecker (Wien