Modelling and Simulation Causes of Complexity Dealing with Complexity Multi-Paradigm Modelling. Modelling and Simulation to tackle Complexity

Transcription

1 Modelling and Simulation to tackle Complexity Hans Vangheluwe

2 1 Modelling and Simulation Modelling and Simulation for... The Modelling Relationship 2 Causes of Complexity Large Number of Components Diversity of Components Non-compositional/Emergent Behaviour Uncertainty 3 Dealing with Complexity Multiple Abstraction Levels Optimal Formalism Multi-Formalism Multiple Views/Aspects 4 Multi-Paradigm Modelling

3 Modelling and Simulation for... Simulation... when too costly/dangerous analysis design

4 Modelling and Simulation for... Simulation... real experiment not ethical physical simulation, training

5 Modelling and Simulation for... Simulation... evaluate alternatives

6 Modelling and Simulation for... Simulation... Do it Right the First Time

7 Modelling and Simulation for... essence: shooting problems

8 Modelling and Simulation for... defining a hit Height (m) 10 5 origin (0, 2) θ target (30, 1) Distance (m)

9 Modelling and Simulation for... optimizing a performance metric

10 Modelling and Simulation for... optimal solution... s

11 Modelling and Simulation for... Modelling/Simulation... and code/app Synthesis

12 Modelling and Simulation for... The spectrum of uses of models Documentation Formal Verification (all models, all behaviours) Model Checking (one model, all behaviours) Test Generation Simulation (one model, one behaviour)... calibration, validation, optimization,... Application Synthesis

13 Modelling and Simulation for... Requirements ( What? ) Design ( How? ) Detached or Semi-detached Style (classical, modern,... ) Number of Floors Number of rooms of different types (bedrooms, bathrooms,... ) Garage, Storage,... Cellar Energy-saving measures...

14 Modelling and Simulation for... System Boundaries System to be built/studied Environment with which the system interacts

15 Modelling and Simulation for... System vs. Plant

16 The Modelling Relationship REALITY MODEL Real-World entity Base Model GOALS only study behaviour in experimental context System S within context Model M Model Base a-priori knowledge experiment within context simulate = virtual experiment Experiment Observed Data validation Simulation Results Modelling and Simulation Process

17 The Modelling Relationship Frame Input Variables System (real or model) Frame Output Variables Experimental Frame generator acceptor transducer set of all contexts in which model is valid includes experiment descriptions: parameters, initial conditions re-use, testing

18 Dealing with Complexity

19 Large Number of Components Crowds

20 Large Number of Components Number of Components hierarchical (de-)composition

21 Diversity of Components Diversity of Components: Power Window

22 Diversity of Components Diversity of Components: Paper Mill

23 CFA Diversity of Components Paper Mill Model PaperPulp mill Waste Water Treatment Plant System of WWTP and Stormwater tanks (DEVS) M,S M,S M,S WWTP (DESS) M,S Switch Mixing Aeration Sedimentation M,S Q Effluent M,S Influent Activated sludge unit (DESS) Clarifier (DESS) Q M,S M,S M,S Input function Recycle (return) flow Output function Stormwater tank 1 Input/Output function Stormwater tank 2 overflow fish GE X EDRF + GF X CFF RRA X + algae Fish Farm

24 Non-compositional/Emergent Behaviour Non-compositional/Emergent Behaviour

25 Non-compositional/Emergent Behaviour Engineered Emergent Behaviour

26 Uncertainty Often related to level of abstraction: for example continuous vs. discrete uncertainty imprecise not rigorous

27 Guiding principle ( physics: principle of minimal action) minimize accidental complexity, only essential complexity remains Fred P. Brooks. No Silver Bullet Essence and Accident in Software Engineering. Proceedings of the IFIP Tenth World Computing Conference, pp ,

28 Solutions multiple abstraction levels optimal formalism multiple formalisms multiple views

29 Multiple Abstraction Levels Different Abstraction Levels properties preserved

30 Multiple Abstraction Levels Levels of Abstraction/Views: Morphism model M_t abstraction M_d simulation trajectory traj_t detailed (technical) level traj_d abstract (decision) level

31 Multiple Abstraction Levels Abstraction Relationship foundation: the information contained in a model M. Different questions (properties) P = I(M) which can be asked concerning the model. These questions either result in true or false. Abstraction and its opposite, refinement are relative to a non-empty set of questions (properties) P. If M 1 is an abstraction of M 2 with respect to P, for all p P: M 1 = p M 2 = p. This is written M 1 P M 2. M 1 is said to be a refinement of M 2 iff M 1 is an abstraction of M 2. This is written M 1 P M 2.

32 Optimal Formalism Most Appropriate Formalism

33 Optimal Formalism Forrester System Dynamics model of Predator-Prey interaction uptake_predator loss_prey Grazing_efficiency prey_surplus_br predator_surplus_dr Predator Prey 2 species predator prey system

34 Optimal Formalism Causal Block Diagram model of Harmonic Oscillator x0 1.0 K IC x I OUT 1.0 y0 PLOT IC y

35 Optimal Formalism Petri Net model of Producer Consumer 1 P.Calculating 1 Wait4Prod Produce 0 Buffer Rem.from buffer 0 Wait4Cons 0 C.Calculating Put in Buffer 1 Buffer p Consume

36 Optimal Formalism GPSS model of Telephone Exchange Function: 1 LNKS 12 FN1 10 V2 2 R PH1 0 1 V1 PH 1 LNKS LR PH1 LR PH2 R PH1 LNKS 2 V1 H S PH2 P1 NE P2 120 FN1 1 S PH1

37 Multi-Formalism Multiple Formalisms: Power Window

38 Multi-Formalism Components in Different Formalisms

39 Multi-Formalism Controller, using Statechart(StateFlow) formalism

40 Multi-Formalism Mechanics subsystem

41 Multiple Views/Aspects Multiple (consistent!) Views (in Formalisms) (work by Esther Guerra and Juan de Lara)

42 Multiple Views/Aspects View: Runtime Diagram

43 Multiple Views/Aspects View: Events Diagram

44 Multiple Views/Aspects View: Protocol Statechart

45 Multiple Views/Aspects No Free Lunch! Solutions often introduce their own accidental complexity multiple abstraction levels (need morphism) optimal formalism (need precise meaning) multiple formalisms (need relationship) multiple views (need consistency)

46 Multi-Paradigm Modelling ( minimize accidental complexity ) at the most appropriate level of abstraction using the most appropriate formalism(s) Differential Algebraic Equations, Petri Nets, Bond Graphs, Statecharts, CSP, Queueing Networks, Lustre/Esterel,... with transformations as first-class models Pieter J. Mosterman and Hans Vangheluwe. Computer Automated Multi-Paradigm Modeling: An Introduction. Simulation 80(9): , September Special Issue: Grand Challenges for Modeling and Simulation.