The Modelling and Simulation Process 1. History of Modelling and - PowerPoint PPT Presentation

The Modelling and Simulation Process 1. History of Modelling and Simulation 2. Modelling and Simulation Concepts 3. Levels of Abstraction 4. Experimental Frame 5. Validation 6. Studying a mass-spring system 7. The Modelling and Simulation Process Hans Vangheluwe hv@cs.mcgill.ca Modelling and Simulation: M&S Process 1/34

Modelling and simulation: past (1950–): Numerical simulations: numerical analysis, statistical analysis, simulation languages (CSSL, discrete-event world views). focus: performance, accuracy (1981–): Artificial Intelligence: model = knowledge representation Use AI techniques in modelling, AI uses simulation (“deep” knowledge) focus: knowledge (1988–): Object-oriented modelling and simulation focus: object orientation, later “agents”, non-causal modelling Hans Vangheluwe hv@cs.mcgill.ca Modelling and Simulation: M&S Process 2/34

Modelling and simulation: past, present, future (1993–): Multi-formalism, Multi-paradigm (2001 –) 1. Do it right (optimally) the first time (market pressure) 2. Complex systems: multi-formalism 3. Hybrid: continuous-discrete, hardware/software 4. Exchange (between humans/tools) and re-use (validated model) 5. User focus: do not expect user to know details (software: glueing of components), need for tools Hans Vangheluwe hv@cs.mcgill.ca Modelling and Simulation: M&S Process 3/34

REALITY MODEL GOALS Real-World Base entity Model only study behaviour in experimental context within context Model Base System S Model M a-priori knowledge experiment simulate within context = virtual experiment validation Experiment Simulation Results Modelling and Simulation Observed Data Process Hans Vangheluwe hv@cs.mcgill.ca Modelling and Simulation: M&S Process 4/34

Behaviour (homo)morphism modelling/abstraction Real System Abstract Model experiment virtual experiment abstraction Experiment Results Simulation Results Hans Vangheluwe hv@cs.mcgill.ca Modelling and Simulation: M&S Process 5/34

Verification and Validation Cause System Effect Conceptual Model Validation Structural Behavioural Conceptual Validation Validation Model Verification Simulation Input Output Model Carl Popper: Falsification, Confidence Hans Vangheluwe hv@cs.mcgill.ca Modelling and Simulation: M&S Process 6/34

Formulated Problem formulated problem NO Type III contains Error actual problem ? YES YES credible NO simulation model ? actual problem actual problem has a credible solution has no credible solution credibility credibility NO NO of simulation results of simulation results certified certified ? ? YES YES simulation simulation NO NO results results accepted accepted ? ? YES YES Type I Type II Error Error Successful Type I Error Unsuccessful Type II Error ending ending ending Ending Hans Vangheluwe hv@cs.mcgill.ca Modelling and Simulation: M&S Process 7/34

� ✁ � ✁ System, Base Model, Lumped Model D BaseModel D RealSystem D LumpedModel E D RealSystem E Hans Vangheluwe hv@cs.mcgill.ca Modelling and Simulation: M&S Process 8/34

✂ Experimental Frame Structure System Frame Output Frame Input (real or model) Variables Variables Experimental Frame generator acceptor transducer Programming Language Types, Pre/Post-conditions Hans Vangheluwe hv@cs.mcgill.ca Modelling and Simulation: M&S Process 9/34

Models and matching Experimental Frames "applies to" general "generalization" "generalization" restricted more restricted Models Experimental Frames Hans Vangheluwe hv@cs.mcgill.ca Modelling and Simulation: M&S Process 10/34

✆ ☎ ✁ ✁ � ✆ ☎ ✁ ✄ ✁ ✁ � ✁ � Experimental Frame and Validity Replicative Validity ( : within accuracy bounds): D LumpedModel E D BaseModel E Predictive Validity: F LumpedModel E F BaseModel E Structural Validity (morphism ): LumpedModel E BaseModel E Simulator Verification: D Simulator D LumpedModel Hans Vangheluwe hv@cs.mcgill.ca Modelling and Simulation: M&S Process 11/34

Modelling (and Simulation) Choices 1. System Boundaries and Constraints: Experimental Frame (EF) 2. Level of Abstraction 3. Formalism(s) 4. Level of Accuracy Hans Vangheluwe hv@cs.mcgill.ca Modelling and Simulation: M&S Process 12/34

✝ System under study: T l controlled liquid closed fill empty is_full is_empty is_cold heat is_hot off cool Hans Vangheluwe hv@cs.mcgill.ca Modelling and Simulation: M&S Process 13/34

✞ ✞ ✞ System Boundaries (Experimental Frame) Inputs: liquid flow rate, heating/cooling rate Outputs: observed level, temperature Contraints: no overflow/underflow, one phase only (no boiling) Hans Vangheluwe hv@cs.mcgill.ca Modelling and Simulation: M&S Process 14/34

☞ ☞ ☞ ☞ ☞ ☞ ☞ ☞ ☞ ☞ ☞ ☞ ✌ ☞ ☞ ☛ ☞ ☞ ☞ ☞ ☞ ☞ ✓ ☞ ✍ ✒ ✏ ✆ ✑ ☞ ✆ ✎ ✆ ✒ ✟ ✕ ✠ ✑ ✠ ✆ ✠ ✒ ✔ ✠ ✑ ✠ ✠ ✡ ✒ ✕ ✠ ✑ ✠ ✆ ✒ ✠ ✔ ✡ ✑ ✡ ✆ ✏ Abstraction: detailed (continuous) view, ALG + ODE formalism Inputs (discontinuous hybrid model): Emptying, filling flow rate φ Temperature of inflowing liquid T in Rate of adding/removing heat W dT 1 W φ T T in dt l c ρ A Parameters: dl φ dt Cross-section surface of vessel A is low l l low Specific heat of liquid c is high l l high Density of liquid ρ State variables: is cold T T cold Temperature T is hot T T hot Level of liquid l Outputs (sensors): is low is high is cold is hot Hans Vangheluwe hv@cs.mcgill.ca Modelling and Simulation: M&S Process 15/34

Abstraction: high-level (discrete) view, FSA formalism level cool cool (cold,full) (T_ib,full) (hot,full) heat heat full empty fill l_in_between (cold,l_ib) (T_ib,l_ib) (hot,l_ib) empty fill (cold,empty) (T_ib,empty) (hot,empty) empty temperature cold T_in_between hot Hans Vangheluwe hv@cs.mcgill.ca Modelling and Simulation: M&S Process 16/34

Levels of abstraction: trajectories (behaviour) level heat Discrete State Trajectory full on off Continuous State Trajectory fill heat l_in_between off off fill empty off on temperature cold T_in_between hot on off of is_cold sensor is_full sensor off off on is_hot sensor is_empty sensor Hans Vangheluwe hv@cs.mcgill.ca Modelling and Simulation: M&S Process 17/34

✞ ✞ ✞ Levels of accuracy Depends on “equality” metric (definition of accuracy) Depends on choice of formalism Depends on choice of numerical approximation Hans Vangheluwe hv@cs.mcgill.ca Modelling and Simulation: M&S Process 18/34

Levels of abstraction: behaviour morphism model M_t M_d abstraction simulation trajectory traj_t traj_d detailed abstract (technical) level (decision) level Hans Vangheluwe hv@cs.mcgill.ca Modelling and Simulation: M&S Process 19/34

A Modelling and Simulation Exercise: the Mass-Spring system WALL Mass m [kg] RestLength [m] WALL Mass m [kg] position x [m] Hans Vangheluwe hv@cs.mcgill.ca Modelling and Simulation: M&S Process 20/34

✞ ✞ ✞ Knowledge Sources A Priori Knowledge: Laws of Physics Goals, Intentions: Predict trajectory given Initial Conditions, “optimise” behaviour, . . . 1. Analysis 2. Design 3. Control Measurement Data Hans Vangheluwe hv@cs.mcgill.ca Modelling and Simulation: M&S Process 21/34

Measured Data Hans Vangheluwe hv@cs.mcgill.ca Modelling and Simulation: M&S Process 22/34

✞ ✞ ✞ ✞ Experimental Frame Room Temperature, normal humidity, . . . Frictionless, Ideal Spring, . . . Apply deviation from rest position Observe position as function of time Hans Vangheluwe hv@cs.mcgill.ca Modelling and Simulation: M&S Process 23/34

✞ ✏ ✞ ✞ ✖ Structure Characterisation n 1 -order polynomial will perfectly fit n data points Ideal Spring: Feature = maximum amplitude constant Spring with Damping: Feature = amplitute decreases Ideal Spring Hans Vangheluwe hv@cs.mcgill.ca Modelling and Simulation: M&S Process 24/34

✗ ✆ ✏ ✆ ✆ ✏ Building the model from a-priori knowledge Newton’s Law M d 2 ∆ x F dt Ideal Spring F K ∆ x d 2 ∆ x K M ∆ x dt 2 Hans Vangheluwe hv@cs.mcgill.ca Modelling and Simulation: M&S Process 25/34

Model representation CLASS Spring "Ideal Spring": DAEmodel := { OBJ F_left: ForceTerminal, OBJ F_right: ForceTerminal, OBJ RestLength: LengthParameter, OBJ SpringConstant: SCParameter, OBJ x: LengthState, OBJ v: SpeedState, F_left - F_right = - SpringConstant * (x - RestLength), DERIV([ x, [t,] ]) = v, EF_assert( x - RestLenght < RestLength/100), }, Hans Vangheluwe hv@cs.mcgill.ca Modelling and Simulation: M&S Process 26/34

✞ ✞ From Model to Simulation Block-diagrams analog computers, Continuous System Modelling Program (CSMP) From (algebraic) equation to Block Diagram Higher order differential equations Hans Vangheluwe hv@cs.mcgill.ca Modelling and Simulation: M&S Process 27/34

Time-slicing Simulator Hans Vangheluwe hv@cs.mcgill.ca Modelling and Simulation: M&S Process 28/34