Constraint

SysMLv1 Parametric Diagram of the Effectiveness-NTU Method for a finned tube cross flow air conditioner heat exchanger

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Tutorial

[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

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SECTION: Miscellaneous examples of applications of Webel libraries for Mathematica to air conditioners and heat exchangers. With SysMLv1 models.

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SysML Parametric Diagram

Webel: SysML4Mathematica: POLICY: Handle flow sign changes via a single negative (not duplicated and "adjusted" algebra). This strategy may come at a very slight performance cost (for benefit of more robustness).

Cameo Simulation Toolkit: You can use Mathematica as an external maths engine to share maths between an OpaqueBehavior and a ConstraintBlock using custom auto-loaded Mathematica functions (keeps a project nice and DRY and respects Single Source of Truth)

HOWTO: MagicDraw/Cameo: v2022Refresh1: JDK 11 download compatible with the modelling tools AND Apple Silicon (ARM) machines (such as M1 Max)

SysMLv1.x: Limitation: The 'body' (maths formula) of an OpaqueBehavior can't be synchronised (shared) with the 'constraint' of a ConstraintBlock (directly in the SysML model). Can lead to a WET (not DRY) model and breaks Single Source of Truth!

Webel: SysML4Mathematica: TIP: Representing Mathematica functions as SysML ConstraintBlocks modelled in SysML Parametric Diagrams and as Activities in SysML Activity Diagrams is super for analysing the dependencies between functions and their arguments!

GOTCHA/BUG: Cameo Simulation Toolkit v2021xR1 + Mathematica: Delegation to Mathematica from ConstraintBlocks FAILS if any of the input or output parameters are larger than 99999 because they get interpreted as 1.0e5 and that trips something! Aarrrggggh!

HOWTO access custom (user-defined) Mathematica functions using Mathematica v13.2 as an external maths engine for SysML Parametrics (ConstraintBlocks) in Magic Model Analyst (Cameo Simulation Toolkit) versions 2021x, 2021xR1, 2022xR1

Mathematica + Magic Model Analyst (Cameo Simulation Toolkit) for SysML Parametrics: GOTCHA: You must use a regular '=' on the SysML side, not the Mathematica '==' (or it will be intepreted as a constraint condition to test, not an equation to solve).

HOWTO use Mathematica v12.3.2 as an external maths engine for SysML Parametrics (ConstraintBlocks) in Magic Model Analyst (Cameo Simulation Toolkit) versions 2021x, 2021xR1, 2022xR1

Interaction - Predation

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Tutorial

TRAIL: SysML+SysPhS vs Modelica By Example in MagicDraw/Cameo SysML [tested with the Wolfram SystemsModeler for Modelica]

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07. Components [MOST]

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SysML Block Definition Diagram (BDD)

SysML Parametric Diagram

SinkOrSource - Reproduction - Starvation

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Tutorial

TRAIL: SysML+SysPhS vs Modelica By Example in MagicDraw/Cameo SysML [tested with the Wolfram SystemsModeler for Modelica]

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07. Components [MOST]

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SysML Block Definition Diagram (BDD)

SysML Parametric Diagram

UngroundedGearComparison - comparison

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Tutorial

TRAIL: SysML+SysPhS vs Modelica By Example in MagicDraw/Cameo SysML [tested with the Wolfram SystemsModeler for Modelica]

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07. Components [MOST]

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SysML Block Definition Diagram (BDD)

SysML Internal Block Diagram (IBD)

SysML Parametric Diagram

GroundedGear - comparison

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Tutorial

TRAIL: SysML+SysPhS vs Modelica By Example in MagicDraw/Cameo SysML [tested with the Wolfram SystemsModeler for Modelica]

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07. Components [MOST]

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SysML Block Definition Diagram (BDD)

SysML Internal Block Diagram (IBD)

SysML Parametric Diagram

SMD_WithBacklash

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Tutorial

TRAIL: SysML+SysPhS vs Modelica By Example in MagicDraw/Cameo SysML [tested with the Wolfram SystemsModeler for Modelica]

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07. Components [MOST]

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SysML Block Definition Diagram (BDD)

SysML Internal Block Diagram (IBD)

SysML Parametric Diagram

SMD

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Tutorial

TRAIL: SysML+SysPhS vs Modelica By Example in MagicDraw/Cameo SysML [tested with the Wolfram SystemsModeler for Modelica]

Section

07. Components [MOST]

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SysML Block Definition Diagram (BDD)

SysML Internal Block Diagram (IBD)

Compliant - RotationalInertia - Spring - Damper - Ground

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Tutorial

TRAIL: SysML+SysPhS vs Modelica By Example in MagicDraw/Cameo SysML [tested with the Wolfram SystemsModeler for Modelica]

Section

07. Components [MOST]

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SysML Block Definition Diagram (BDD)

Basic Rotational Components - TwoFlange

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Tutorial

TRAIL: SysML+SysPhS vs Modelica By Example in MagicDraw/Cameo SysML [tested with the Wolfram SystemsModeler for Modelica]

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07. Components [MOST]

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SysML Block Definition Diagram (BDD)

TwoPin - SwitchedRLC

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Tutorial

TRAIL: SysML+SysPhS vs Modelica By Example in MagicDraw/Cameo SysML [tested with the Wolfram SystemsModeler for Modelica]

Section

07. Components [MOST]

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SysML Block Definition Diagram (BDD)

Resistor - Capacitor - Inductor - StepVoltage - Ground

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Tutorial

TRAIL: SysML+SysPhS vs Modelica By Example in MagicDraw/Cameo SysML [tested with the Wolfram SystemsModeler for Modelica]

Section

07. Components [MOST]

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SysML Block Definition Diagram (BDD)

Electrical Components - TwoPin

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Tutorial

TRAIL: SysML+SysPhS vs Modelica By Example in MagicDraw/Cameo SysML [tested with the Wolfram SystemsModeler for Modelica]

Section

07. Components [MOST]

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SysML Block Definition Diagram (BDD)

SysML Parametric Diagram

MagicDraw/Cameo v19SP3+SysPhS-1.1: On export to Modelica sometimes repeats parts of an equation into an extending model.

MagicDraw/Cameo v19SP3+SysPhS-1.1: Does not cleanly export INLINE Modelica 'if/then/else' statements (a.k.a. "switching" form)

MagicDraw/Cameo v19SP3+SysPhS-1.1: Does not cleanly export Modelica 'when/then' statements

MagicDraw/Cameo: SysML Parametrics: To colour instance table cells to indicate broken constraints you need to create at least one Simulation Configuration Diagram, which loads a validation profile with colour coding rules.

SysPhS-1.1: Annex A.5: The BDD Figure 74 and Parametric Diagram Figure 84 for block RelativeHumidityCalculationConstraint are missing PhSConstant 'c2'. Compare with the constraint {der(x)=((press/satVap)-change)/c2} in BDD Figure 79.

SysPhS-1.1: p.81: 'resistance:ViscousResistance' (in Figure 60) has to be treated as a PhSVariable not a PhSConstant, otherwise get an invalid system with 6 variables and 7 equations.

Parametric diagrams: Figure 62, Figure 63

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Tutorial

TRAIL: SysPhS-1.1 Annex A examples in MagicDraw/Cameo SysML vs Modelica (Wolfram SystemsModeler)

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Annex A.4: Hydraulics

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SysML Parametric Diagram

Figure 62 and Figure 63 show the parametric diagrams of the tank and the pipe, respectively.

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Binding connectors link constraint parameters to simulation variables and constants, indicating their values must be the same.

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Component parametric diagrams show properties typed by constraint blocks (constraint properties), as well as component and port simulation variables and constants.

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Equations in constraint blocks are applied to components using binding connectors in component parametric diagrams.

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Also, the fluid flow in the tank, fluidFlow, is related to the change in the fluid height level fluidHeight over time and the cross-sectional surface area of the tank, surfaceArea.

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The tank constraints specify that the pressure in the tank, pressure depends on the height of the fluid level in the tank, fluidHeight, as well as properties of the fluid, fluidDensity.

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The sum of the fluid flow rates going through the two pipe openings is zero (the fluid is assumed to be incompressible).

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The magnitude of fluid flow rate through the pipe fluidFlow is the same as the magnitude of flow rates opening1FluidFlow and opening2FluidFlow going through the pipe’s openings, though the values differ in sign.

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The fluid flow rate through the pipe, fluidFlow, is proportional to the pressure difference by the constant resistance, which depends on the geometric properties of the pipe as well as fluidic properties.

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The pipe constraints specify that the pressure pressureDiff across it is equal to the difference of fluid pressures opening1Pressure and opening2Pressure at each end of the pipe.

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In this example, constraint blocks PipeConstraint and TankConstraint define parameters and equations for pipes and tanks, respectively, as shown in Figure 61.

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Equations define mathematical relationships between the values of numeric variables. Equations in SysML, are constraints in constraint blocks that use properties of the blocks (parameters) as variables.

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BDD: Figure 61: Hydraulics model constraint blocks

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Tutorial

TRAIL: SysPhS-1.1 Annex A examples in MagicDraw/Cameo SysML vs Modelica (Wolfram SystemsModeler)

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Annex A.4: Hydraulics

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SysML Block Definition Diagram (BDD)

Each type of component has its own behaviors, defined as constraints ...

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Figure 52 through Figure 57 show parametric diagrams for the source, amplifier, high-pass fil[t]er, low-pass filter, mixer, and sink, respectively.

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Binding connectors link constraint parameters to simulation variables and constants, indicating their values must be the same.

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Component parametric diagrams show properties typed by constraint blocks (constraint properties), as well as component and port simulation variables and constants.

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Equations in constraint blocks are applied to components using binding connectors in component parametric diagrams.

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The source constraint specifies a sine wave signal with the parameter amp as its amplitude. The sink constraint displays (scopes) the output signal from the signal processor.

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The mixer constraint specifies the relationship between its one output and the two inputs that come from the low-pass and high-pass filters. The constraint defines the output to be the average of the inputs.

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The amplifier changes the signal strength by a factor gain, the low-pass filter eliminates the high-frequency components of the incoming signal, and the high-pass filter eliminates the low-frequency components of the signal.

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The amplifier, low-pass fil[t]er, and high-pass filter constraints show the input-output relationship of these components as the signal passes through them.

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In this example, a constraint block BinarySignalComponentConstraint defines the parameters for one input (ip) and one output (op), common to amplifiers, low-pass filters, and high-pass filters, as shown in Figure 51.

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Equations define mathematical relationships between the values of numeric variables. Equations in SysML, are constraints in constraint blocks that use properties of the blocks (parameters) as variables.

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Each kind of component has its own behaviors, defined as constraints ...

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Parametric diagrams: Figure 52, Figure 53, Figure 54, Figure 55, Figure 56, Figure 57

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Tutorial

TRAIL: SysPhS-1.1 Annex A examples in MagicDraw/Cameo SysML vs Modelica (Wolfram SystemsModeler)

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Annex A.3: Signal Processor

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SysML Parametric Diagram

BDD: Figure 51: Signal processing system constraint blocks

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Tutorial

TRAIL: SysPhS-1.1 Annex A examples in MagicDraw/Cameo SysML vs Modelica (Wolfram SystemsModeler)

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Annex A.3: Signal Processor

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SysML Block Definition Diagram (BDD)

SysML/SysPhS + Modelica: The variable 'time' is known to Modelica and need not be explicitly declared as a constraint parameter for a Constraint on a SysML ConstraintBlock

The source constraint defines the voltage across it as a sine wave with the parameter amp as its amplitude.

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The source constraint defines the circuit’s electrical source. The ground constraint specifies that the voltage at the ground pin is zero.

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The constraints for the resistor, capacitor, and inductor specify the voltage/current relationship with resistance, capacitance, and inductance, respectively.

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The sum of the current going through the two pins adds up to zero (one is the negative of the other), because the components do not create, destroy, or store charge.

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The current i through the component is equal to the current going through the positive pin.

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These specify that the voltage v across the component is equal to the difference between the voltage at the positive and negative pins. The current i through the component is equal to the current going through the positive pin.

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In this example, a constraint block BinaryElectricalComponentConstraint defines parameters and constraints common to resistors, inductors, capacitors, and sources, as shown in Figure 40.

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Equations define mathematical relationships between the values of numeric variables. Equations in SysML, are constraints in constraint blocks that use properties of the blocks (parameters) as variables.

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Parametric diagrams: Figure 41, Figure 42, Figure 43, Figure 44, Figure 45

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Tutorial

TRAIL: SysPhS-1.1 Annex A examples in MagicDraw/Cameo SysML vs Modelica (Wolfram SystemsModeler)

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Annex A.2: Electric Circuit

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SysML Parametric Diagram

BDD: Figure 40: Circuit constraint blocks

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Tutorial

TRAIL: SysPhS-1.1 Annex A examples in MagicDraw/Cameo SysML vs Modelica (Wolfram SystemsModeler)

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Annex A.2: Electric Circuit

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SysML Block Definition Diagram (BDD)

f1 is replaced by p1.f, v1 is replaced by p1.lV, x is replaced by lengthchg, k is replaced by springcst, v is replaced by velocitydiff, f is replaced by forcethru, v2 is replaced by p2.v, and f2 is replaced by p2.f.

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The following Modelica code corresponds to Figure 26. It has five equations from the SysML constraint block. SysML parameter names are replaced in the Modelica equations according the bindings in Figure 14 [ERROR]:

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(and flow properties in SysML property paths leading to PhSVariables on conserved quantity kinds are omitted in Modelica, see Subclause 10.7.8).

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In a SysML block with constraint properties, the constraints correspond to the same equations in Modelica ... except the SysML parameters in those equations correspond in Modelica to the properties they are bound to in SysML

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Figure 26: Constraint block for physical interaction in SysML

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Tutorial

TRAIL: SysPhS-1.1 specification body figures in MagicDraw/Cameo SysML vs Modelica [using Wolfram SystemsModeler]

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SysML Block Definition Diagram (BDD)

SysML Parametric Diagram

SysML parameter names are replaced in the Modelica equations according to the bindings in Figure 13 [ERROR]: f is replaced by u, pos is replaced by y, x is replaced by position, k is replaced by springcst, v is replaced by velocity, m is replaced by mass.

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The following Modelica code corresponds to Figure 25. It has three equations from the constraint block.

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In a SysML block with constraint properties, the constraints correspond to the same equations in Modelica ... except the SysML parameters in those constraints correspond in Modelica to the properties they are bound to in SysML.

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Figure 25: Constraint block for signal flow in SysML

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Tutorial

TRAIL: SysPhS-1.1 specification body figures in MagicDraw/Cameo SysML vs Modelica [using Wolfram SystemsModeler]

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SysML Block Definition Diagram (BDD)

SysML Parametric Diagram

MagicDraw SysML/Cameo: GOTCHA: A Constraint created and applied to a ConstraintBlock via the sidebar menu is NOT owned by the ConstraintBlock!

Webel Twin Pattern: DigitalTwin: The multiplicity of 'digitalEntity:@Entity' and 'physicalEntity:PhysicalEntity' MUST be [1] when the DigitalTwin is in the state Attached, the @Entity is in the state Bound, and the PhysicalEntity is in the state Exists.

Webel: SysMLv2: WISHLIST: Suggest declare an custom Stereotype as 'cascading' then behave likes constraint rules for Block

Optical images, image sensors, image data

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Tutorial

TRAIL: Webel SysML Parsing Analysis example: Optical telescopes from Wikipedia: Structure and port-based light flow model

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SysML Package Diagram

Radio frequencies (just a quick look)

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Tutorial

TRAIL: Webel SysML Parsing Analysis example: Optical telescopes from Wikipedia: Structure and port-based light flow model

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SysML Block Definition Diagram (BDD)

Our first Parsing Analysis diagram about telescopes

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Tutorial

TRAIL: Webel SysML Parsing Analysis example: Optical telescopes from Wikipedia: Structure and port-based light flow model

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SysML Block Definition Diagram (BDD)

An abstract Q(u)ark for M(u)ster M(u)ark

This content has been marked as discussing an ADVANCED topic!

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Tutorial

TRAIL: Webel SysML Parsing Analysis example: A particle physics taxonomy from Wikipedia

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SysML Block Definition Diagram (BDD)

From hadron to meson Package Diagrams and focus BDDs

This content has been marked as discussing an ADVANCED topic!

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Tutorial

TRAIL: Webel SysML Parsing Analysis example: A particle physics taxonomy from Wikipedia

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SysML Block Definition Diagram (BDD)

SysML Package Diagram

The minimum on mesons

This content has been marked as discussing an ADVANCED topic!

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Tutorial

TRAIL: Webel SysML Parsing Analysis example: A particle physics taxonomy from Wikipedia

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SysML Block Definition Diagram (BDD)

Spin-1/2 particles so far

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Tutorial

TRAIL: Webel SysML Parsing Analysis example: A particle physics taxonomy from Wikipedia

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SysML Block Definition Diagram (BDD)

Neutrons and protons are spin-1/2 fermions and baryons

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Tutorial

TRAIL: Webel SysML Parsing Analysis example: A particle physics taxonomy from Wikipedia

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SysML Block Definition Diagram (BDD)

Leptons as fermions

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Tutorial

TRAIL: Webel SysML Parsing Analysis example: A particle physics taxonomy from Wikipedia

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SysML Block Definition Diagram (BDD)

Lepton types by charge

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Tutorial

TRAIL: Webel SysML Parsing Analysis example: A particle physics taxonomy from Wikipedia

Section

Slide kind

SysML Block Definition Diagram (BDD)

Transition::guard : Constraint [0..1] ... If the guard is true at that time, the Transition may be enabled, otherwise, it is disabled. Guards should be pure expressions without side effects. Guard expressions with side effects are ill formed.

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Unified Modeling Language 2.5.1

Transition::guard : Constraint [0..1] ... A guard is a Constraint that provides a fine-grained control over the firing of the Transition. The guard is evaluated when an Event occurrence is dispatched by the StateMachine. ...

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Unified Modeling Language 2.5.1

The parametric diagram is a new SysML diagram type that describes the constraints among the properties associated with blocks. This diagram is used to integrate behavior and structure models with engineering analysis models such as performance, ...

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OMG Systems Modeling Language (SysML) 1.6

SysML also allows each usage to define context-specific values and constraints associated with the individual usage, such as 25 psi for the front tires and 30 psi for the rear tires.

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OMG Systems Modeling Language (SysML) 1.6

Constraint Properties are a special class of property used to constrain other properties of blocks...

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OMG Systems Modeling Language (SysML) 1.6

MagicDraw/Cameo support for the SysML Parametric Diagram and ConstraintBlocks for equations and mathematics is excellent, and it integrates with powerful maths engines such as Mathematica. It CAN be used on industrial strength real-world projects.

The SysML Parametric Diagram and the ContraintBlock technology for equations and mathematics is clever, powerful, useful, and integrates well with the other model-based engineering aspects of SysML.

MagicDraw/Cameo can parse the 'text' field of some mathematical Requirements and populate the constraint (and also then the constraint parameters) of a ConstraintBlock that refines a Requirement (your mileage varies).

It assumes a constant 100hp at the drive wheels, 4000lb gross vehicle weight, and constant values for Cd and Cf.

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OMG Systems Modeling Language (SysML) 1.6

For illustration purposes, however, the interaction shown in Figure D.35 was generated based on the constraints and parameters of the StraightLineVehicleDynamics constraintBlock, as described in the Figure D.33.

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OMG Systems Modeling Language (SysML) 1.6

The constraints and parameters in Figure D.33 are detailed in Figure D.34 in Block Definition Diagram format. Note the use of valueTypes [ValueTypes] originally defined in Figure D.2.

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OMG Systems Modeling Language (SysML) 1.6

Figure D.34 - Defining Straight-Line Vehicle Dynamics Mathematical Constraints (Definition of Dynamics)

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Tutorial

TRAIL: The SysML-1.6 Hybrid SUV sample and specification diagrams in MagicDraw/Cameo (with annotations) [UNDERGOING UPDATE to SysML1.7]

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Section: SysML-1.6: HSUV sample

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SysML Block Definition Diagram (BDD)

MagicDraw/Cameo: Does not support ConstraintNote: Can't callout the Constraint of the ConstraintBlock of a constraint property into a Note on a Parametric Diagram (show on the constraint property symbol instead)

Figure D.26 defines the various model elements that will be used to conduct analysis in this example. It depicts each of the constraint blocks/equations that will be used for the analysis, and key relationships between them.

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OMG Systems Modeling Language (SysML) 1.6

The context for the usages of constraint blocks shall also be specified in a parametric diagram to maintain the proper namespace for the nested properties.

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OMG Systems Modeling Language (SysML) 1.6

This allows a value property (such as an engine displacement) that may be deeply nested within a containing hierarchy (such as vehicle, power system, engine) to be referenced at the outer containing level (such as vehicle-level equations).

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OMG Systems Modeling Language (SysML) 1.6

A pathname dot notation can be used to refer to nested properties within a block hierarchy.

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OMG Systems Modeling Language (SysML) 1.6

The constrained properties, such as mass or response time, typically have simple value types that may also carry units, quantity kinds, or probability distributions.

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OMG Systems Modeling Language (SysML) 1.6

The usage of a constraint binds the parameters of the constraint, such as F, m, and a, to specific properties of a block, such as a mass, that provide values for the parameters.

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OMG Systems Modeling Language (SysML) 1.6

Parametric diagrams include usages of constraint blocks to constrain the properties of another block.

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OMG Systems Modeling Language (SysML) 1.6

The constraints can be nested to enable a constraint to be defined in terms of more basic constraints such as primitive mathematical operators.

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OMG Systems Modeling Language (SysML) 1.6

Reusable constraint definitions may be specified on block definition diagrams and packaged into general-purpose or domain-specific model libraries. Such constraints can be arbitrarily complex mathematical or logical expressions.

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OMG Systems Modeling Language (SysML) 1.6

Constraint blocks define generic forms of constraints that can be used in multiple contexts. For example, a definition for Newton’s Laws may be used to specify these constraints in many different contexts.

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OMG Systems Modeling Language (SysML) 1.6

A constraint block includes the constraint, such as {F=m*a}, and the parameters of the constraint such as F, m, and a.

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OMG Systems Modeling Language (SysML) 1.6

Such constraints can also be used to identify critical performance parameters and their relationships to other parameters, which can be tracked throughout the system life cycle.

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OMG Systems Modeling Language (SysML) 1.6

Constraint blocks can be used to specify a network of constraints that represent mathematical expressions such as {F=m*a} and {a=dv/dt}, which constrain the physical properties of a system.

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OMG Systems Modeling Language (SysML) 1.6

A constraint block typically defines one or more constraint parameters, which are bound to properties of other blocks in a surrounding context where the constraint is used.

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OMG Systems Modeling Language (SysML) 1.6

A constraint block is a block that packages the statement of a constraint so it may be applied in a reusable way to constrain properties of other blocks.

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OMG Systems Modeling Language (SysML) 1.6

choice – This type of Pseudostate is similar to a junction Pseudostate ... and serves similar purposes, with the difference that the guard Constraints on all outgoing Transitions are evaluated dynamically ...

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Unified Modeling Language 2.5.1

NOTE. Such guard Constraints are evaluated before any compound transition containing this Pseudostate is executed, which is why this is referred to as a static conditional branch.

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Unified Modeling Language 2.5.1

.. a junction Pseudostate ... can be used to split an incoming Transition into multiple outgoing Transition segments with different guard Constraints.

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Unified Modeling Language 2.5.1

fUML-1.4 EXCLUDES Constraint

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