Modeling and simulation of systems Slovak University of Technology Faculty of Material Science and Technology in Trnava

Modelovanie a simulácia systémov Doc. Ing. Pavel Važan, PhD.

Key terms  System  Intentionally defined set of components, relations between them and relations with surroundings.  Arranged variety of entities.  System is a complex which consists of segments (components,...) among which exist relations. When we speak about system we always mean a complicated unity, structure, something that is not randomly compound.  Each system consists of two classes :  Class of elements  Class of relations between elements

Key terms  Element part of the system that is indivisible on the given level  System surroundings is created from non-system elements with certain relationships to the system elements.  System structure given by the set of elements and set of relations.  System behaviour given by relationship between inputs and outputs of system

Key terms  System state Is expressed by quantities which inform about system history (minimal number of information) to determine the behaviour of system in the future.  state variables – describe the state  Dynamic system  is such system which state at the time t depends on the state before the time t.

Key terms  Systems  Deterministic future state is unambiguously determined by initial state  Stochastic behaviour of the system is possible to determine only with certain probability  Continuous systems change of the state happens continuously  Discrete systems state changes discretely

Modeling  Cognition method.  it is experimental information process where observed system is unambiguously has assigned another physical or abstract system. The system is called model.  Model has to be independent on the implementation language and architecture.

Model A model has no inherent value of its own the value of a model is based entirely upon the degree to which it solves someone’s real-world problem.  Models are not universally useful, but are designed for specific purposes.  A great model for the wrong problem will never be used.  Learning to model is better than learning about models

Principles of modeling Simplify, simplify To learn from the past Create a conceptual model Build a prototype Push the User’s Hot Buttons Model to Data Available Separate Data from Software Trust Your Creative Juices Fit Universal Constraints Distil Your Own Commandments

Modeling A model is the result of modeling process. The model is created to analyze real system or to verify future characters of projected systems. Validity question  How does the model represent real system?

What is simulation? It is the process of model design and realization of experiments for the purpose either behavior understanding of system or evaluation of different strategies. (Shannon)

Simulation (Banks) is the imitation of the operation of a real-world process or system over time. Simulation involves the generation of an artificial history of the system, and the observation of that artificial history to draw inferences concerning the operating characteristics of the real system that is represented.. is an indispensable problem-solving methodology for the solution of many real-world problems. Simulation is used to describe and analyze the behavior of a system, ask "what if" questions about the real system, and aid in the design of real systems. Both existing and conceptual systems can be modeled with simulation

Modeling and simulation Real system Model computer Modeling Simulation

Observed system System model Model modification Difference criterion Input System output Model output Difference value Relationship between system and its model

Model classification Models PhysicalMathematical DynamicStatic SimulationAnalytical DiscreteCombinedContinuous

Analytical vs. Simulation models Analytical models provide the results in mathematical forms where variables are parameters of model. The solution for specific model demands the solution of mathematical forms (mathematical equations). Simulation models distinguish from each other mainly in the way of gaining solution values. Values are obtained from model in time by watching. It means that information is recorded from the changes of states of model in given time. This time is completely separated from the real time.

Key terms  Verification  Determines if computer interpretation of conceptual model is right. It is the question: “Does computing model represent conceptual model?”  Validation  Determines if conceptual model for proposal of experiments can substitute real system

Key terms

What is possible to simulate?... Everything that can be mathematically or through other model described. transport production Finances and banking communications Trade and services Biological and medical systems

Simulation answers the questions:  Is it possible to reduce flow time?  Can we sell or produce more products ?  Are our sources exploited sufficiently?  What is „bottleneck“ of our system?  What happens if...?  How much will cost decision?

What is expected from simulation?  Support in decisions at designing of system or its operation  Analysis and optimization of system  Prediction – forward view  Substitution of the real system for training purpose, testing, big danger or big risk