Structural Diagrams: Parametric Diagrams
SysML Structural Diagram Types
Structural Related
Block Definition Diagrams (bdd)
System elements
Internal Block Diagrams (ibd)
Interactions between parts
Package Diagrams (pkg)
structure of the model not the system
Parametric Diagram (par)
mathematical constraints
An Intro to SysML Structural Diagrams
SysML Parametric diagrams are used to represent the numerical relationships between various elements in a system. These diagrams are often used when modeling complex systems, as they provide a way to visualize the relationships between different components. They are also useful for analyzing the effect of changes in one element on the rest of the system.
SysML Parametric diagrams are composed of blocks which represent the different elements of the system and connectors which represent the numerical relationships between the blocks. The connectors are drawn as straight lines with arrows indicating the direction of the relationship, and can be labeled to indicate the type of relationship. For example, an arrow with a plus sign may indicate a positive relationship, while an arrow with a minus sign may indicate a negative relationship.
The numerical relationships between the blocks are expressed as equations, with the equation being written in the connector itself. These equations can consist of any combination of mathematical operators, constants, and functions of the connected blocks. The equations can also be changed to simulate different scenarios, such as different types of inputs or different levels of system performance.
SysML Parametric diagrams are a powerful tool for modeling and analyzing complex systems. They provide a way to quickly visualize the relationships between different components, and also allow for easy simulation of different scenarios. They can be used to help engineers design better systems, as well as to predict the behavior of existing systems.
Parametric Diagram (par) Examples
Definitions of a Parametric Diagram (par)
What is a SysML Parametric Diagram? Several Different Definitions from the Experts
Definition 1:
Parametric diagram (par): An Parametric diagram is a specialization of an Internal Block Diagram (IBD) that enforces mathematical rules (Constraints) defined by Constraint Blocks across the internal Part Value Properties bound by the Constraint Block Parameters.
Binding Connectors (keyword = «equal») between Constraint Block Parameters and internal Part Value Properties effect constraint satisfaction (propagation)
https://sysml.org/sysml-faq/what-is-parametric-diagram.html
Definition 2:
The SysML Parametric Diagram is a type of Internal Block Diagram (with some restrictions) that is used to model equation with parameters. They are an important tool that can be used to describe equations and their parameters and are important when performing trade off analysis and assessing design alternatives as they can be combined into systems of equations and related to Measures of Effectiveness MOEs.
Parametric diagrams describe the usage of constraint blocks and provide a mechanism for integrating engineering analysis such as performance and reliability and other factors of interest with other SysML models and diagrams.
Parametric diagrams define the way that constraint blocks are used to constrain the properties of another block. The usage of a constraint is said to bind the parameters of the constraint (e.g. F=m*a), such as F, m, and a, to specific properties of a block, such as a mass and acceleration, that provide values for the parameters.
Cameo par Toolbar
Elements within a Parametric Diagram
Elements:
The main elements that can appear in Parametric diagrams are:
Constraint Property: The usage of a constraint block. It is denoted with a purple rectangle with rounded corners.
Constraint Parameter: A formal term for a variable that appears in a constraint expression. It is displayed as a small square attached to the boundary on the inside of a constraint property.
Objective Function: A special type of constraint property that has a slightly different icon within Cameo but acts identically to a constraint property. This different icon allows for modelers to recognize quickly that the constraint is important because it's an Objective Function.
Measure of Effectiveness: A special type of constraint property that has a slightly different icon within Cameo but acts identically to a constraint property. This different icon allows for modelers to recognize quickly that the constraint is important because it's an MoE.
The main connectors that can appear in Parametric diagrams are:
Binding Connector: Solid line which maps the value properties to their respective constraint parameters. Acts as an equals sign and can be denoted with the <<equal>> stereotype label.
Constraint Block:
A Constraint Block (notation: rectangle with keyword = «constraint») defines a mathematical rule (Constraint) and rule Parameters, where the latter are bound to Block Value Properties so that changes to one Block Value Property will be propagated to other Block Value Properties in a manner consistent with the mathematical rule.
Note: Constraint blocks are re-usable elements of definition and are only shown on a block definition diagram. The usage of the constraint block, the constraint property can be found on the parametric diagram.
Doctors Waiting Room Wait Time Parametric Example
This example shows a constraint block, "WaitTimeEquation", which has been added as a constraint onto the block, "Doctors Waiting Room". Several value properties, "waitTime" and "numberOfMagazines" have been made on the "Doctors Waiting Room" block. A parametric diagram has been created with the "Doctors Waiting Room" block as the context of the parametric diagram. The value properties are shown as pink rectangles. The usage of the constraint is shown as the purple rectangle. The yellow squares are the variable inputs and outputs of the equation. The Cameo simulation toolkit plugin was used to run a simulation. The simulation window is shown below the picture of the bdd and par diagrams. A user can plug in any value for the "numberOfMagazines" within the simulation window and the "waitTime" will be calculated. In the example, 14 was input and 23.8 was output. The blue values are shown within the parametric diagram for Cameo 2021x and on. Note: this feature is not available for Cameo 2019 SP4.
When to use a Parametric Diagram
Definition 1:
The Parametric diagram can be used to show how the physical properties of a system are constrained by specifying a network of constraints that represent mathematical expressions such as {F=m*a} and {a=dv/dt}.
They can also be used for trade-off analysis, where a Constraint Block can define an objective function used to make a comparison between alternative solutions.
Critical performance parameters and their relationships to other parameters can be modeled, which can then be tracked throughout the system life cycle.
What is the purpose of a Parametric Diagram?
The purpose of Parametric diagrams (PARs) is to enforce mathematical rules across Block Value Properties. When used correctly BDDs + IBDs + PARs are recursively scalable and mathematically simulatable.
