Digital Mission Engineering (DME): Constellation Design and Coverage with ModelCenter (Part 1 of 4)

STK Premium (Space) or STK Enterprise
You can obtain the necessary licenses for this tutorial by contacting AGI Support at support@agi.com or 1-800-924-7244.

This lesson requires version 12.7 of the STK software or newer to complete.

Required product install: The Ansys ModelCenter® model-based systems engineering software and the STK Plugin for ModelCenter are required to complete this tutorial.

ModelCenter installation prerequisites: The ModelCenter software requires the installation of a 64-bit version of Java, a 64-bit implementation of Python 3.x, and the installation of the thrift and six Python packages. See the ModelCenter Installation Prerequisites for more information.

This tutorial was written using version 2026 R1 of the Ansys ModelCenter® model-based systems engineering software.

The results of the tutorial may vary depending on the user settings and data enabled (online operations, terrain server, dynamic Earth data, etc.). It is acceptable to have different results.

Capabilities covered

This lesson covers the following capabilities of the Ansys Systems Tool Kit® (STK®) digital mission engineering software:

  • STK Pro
  • Coverage
  • STK Analyzer
  • STK Analyzer Optimization

Problem statement

Across the industry, the digital engineering process is becoming more complex. Systems of systems are being changed and updated in different stages of the mission life cycle. In this series, you will address these challenges by creating a fully connected digital thread with a common mission environment at the core. You will address this topic in stages: satellite constellations, hypersonic flight, EOIR sensors, communications links, and triggering events and systems. The vision is to integrate the mission environment and operational objectives into the digital thread early and throughout the entire product life cycle. Through digital mission engineering, you are now capable of quickly evaluating the overall mission impact of the smallest change to any component. This session will focus on the concept development phases using the Ansys ModelCenter® model-based systems engineering software. You want to design, test, and optimize a new satellite constellation for persistent stereo coverage of hypersonic vehicles across the world.

Solution

Use the STK software's Coverage capability and the Analyzer capability, which is available with the Ansys ModelCenter® model-based systems engineering software, to conduct trade studies on the satellite constellation's geometry and optimize it based on mission and system requirements. The goal in this exercise is to understand how to maximize the level of global coverage with a network of satellites. The main components you will analyze are the revisit time, which can be considered the gap time, and the number of assets that have visibility to a point on the Earth's surface at a given time. Using the STK Analyzer Optimization capability and the ModelCenter software's trade study capabilities, you can vary parameters of your system to find an ideal configuration.

What you will learn

Upon completion of this tutorial, you will be able to:

  • Build a constellation of satellites using the Satellite Collection object
  • Design a Coverage analysis
  • Utilize relevant Figure of Merit quality metrics
  • Become familiar with the ModelCenter software's workflow
  • View an external trade study file
  • Understand satellite constellation design configurations

Creating a new scenario

First, you must create a new scenario and then build from there.

  1. Launch the STK application ().
  2. Click Create a Scenario in the Welcome to STK dialog box.
  3. Enter the following in the STK: New Scenario Wizard:
    4. Option Value
    Name ImagingConstellation
    Start 13 Feb 2025 16:00:00.000 UTCG
    Stop + 1 day
  4. Click OK when you finish.
  5. Click Save () when the scenario loads. The STK application creates a folder with the same name as your Scenario for you.
  6. Verify the scenario name and location in the Save As dialog box.
  7. Click Save.

Save () often during this lesson!

Downloading a precomputed trade study

This tutorial uses a precomputed trade study. Download it following the steps below.

  1. Download the zipped folder here: https://support.agi.com/download/?type=training&dir=sdf/help&file=DME_Part1_MC_TradeStudy.zip

    If you are not already logged in, you will be prompted to log in to agi.com to download the file. If you do not have an agi.com account, you will need to create one. The user approval process can take up to three (3) business days. Please contact support@agi.com if you need access sooner.

  2. Navigate to the downloaded folder in Windows File Explorer.
  3. Right-click on DME_Part1_MC_TradeStudy.zip.
  4. Select Extract All... in the shortcut menu.
  5. Set the Files will be extracted to this folder: path to your scenario folder (for example, C:\Users\<username>\Documents\STK_ODTK 13\ImagingConstellation).
  6. Click Extract.
  7. Navigate to your scenario folder.
  8. The DME_OptStudy3.tstudy file will be in your scenario folder.

Creating a Walker-type Satellite Collection

A Satellite Collection object models a group of satellites as a single object in the Object Browser. The associated satellites do not appear in the Object Browser, but are available for analysis purposes within other computational tools such as the STK software's Coverage capability, CommSystem objects, the Deck Access tool, and the Advanced CAT tool.

Inserting a Satellite Collection object

Start by inserting a Satellite Collection object into your scenario.

  1. Bring the Insert STK Objects tool () to the front.
  2. Select SatelliteCollection () in the Select An Object To Be Inserted list.
  3. Select Insert Default () in the Select A Method list.
  4. Click Insert. . ..
  5. Right-click on SatelliteCollection1 () in the Object Browser.
  6. Select Rename in the shortcut menu.
  7. Rename SatelliteCollection1 () Walker_Collection.

Setting the Walker type subset

The default Satellite Collection definition is a Walker-type constellation. The Walker selection provides a constellation of satellites distributed in a series of altitude shells. Each shell contains evenly spaced orbital planes and Walker populates each orbital plane with evenly spaced satellites. All the satellites in a shell have the same period and inclination. Walker evenly spaces the ascending nodes of the orbital planes over a range (angle spread) of right ascensions (RAAN). You can generate multiple shells within a single Satellite Collection object.

  1. Right-click on Walker_Collection () in the Object Browser.
  2. Select Properties () in the shortcut menu.
  3. Select the Basic - Definition page when the Properties Browser opens.

    4. You can see that Walker is selected as the default Type.

  4. Select the Shells - Name - 1 row in the Walker Properties panel.
  5. Click Edit selected shell () in the Shells toolbar.
  6. Enter Walker Group in the Shell Name field when the Edit Shell dialog box opens.
  7. Set the following options in the order shown in Shell Properties panel:
    8. Option Value
    Inter Plane Phase Increment 0
    Planes 1
    Satellites in Planes (Slots) 1
  8. Set the following orbital parameters in the Plane 1 : Slot 1 panel:
    9. Option Value
    Semi-Major Axis (a) 6880 km
    Inclination (i) 50 deg
  9. Click Save Changes to apply your changes and to close the Edit Shell dialog box.
  10. Click Apply to accept your changes and to keep the Properties Browser open.

Setting the subset marker size

You can control the graphical display of a satellite collection. The Satellite Collection Graphics Attributes cover both the 2D and 3D Graphics window attributes. In this case, increase the marker size to make the satellites easier to see.

  1. Select the Graphics - Attributes page.
  2. Double-click in the AllSatellites - Marker Size cell.
  3. Enter 10 as the Marker Size value.
  4. Click OK to accept your changes and to close the Properties Browser.

Using a Coverage Definition object

You are now ready to model a coverage analysis over the Earth using a Coverage Definition object. The STK software's Coverage capability enables you to analyze global or regional coverage provided by one or more assets while considering all access constraints. A Coverage Definition object enables you to define and maintain an area of coverage, to define the objects providing coverage for the area, and to calculate accesses to the region.

Inserting a Coverage Definition object

Start by inserting a Coverage Definition object using the Define Properties method.

  1. Bring the Insert STK Objects tool () to the front.
  2. Select Coverage Definition () in the Select An Object To Be Inserted list.
  3. Select the Define Properties () method in the Select A Method list.
  4. Click Insert. . ..

Changing the grid area of interest and point granularity

Coverage analyses are based on the accessibility of assets (objects that provide coverage) and geographical areas. The combination of the geographical area, the regions within that area, and the points within each region is called the coverage grid. The statistical data computed during a coverage analysis are based on a set of locations, or points, which span the specified grid area of interest. Points have specific geographical locations, and the STK application uses them in the computation of asset availability. The angular distance between the grid points is called the point granularity.

Use the Grid properties to define the location of your coverage grid to fall between specified minimum and maximum latitude bounds, with a point granularity that balances for accuracy and computation time.

  1. Select the Basic - Grid page when the Properties Browser opens.
  2. Enter 60 deg in the Max. Latitude field in the Grid Area of Interest panel.
  3. Enter 10 deg in the Lat/Lon field in the Point Granularity panel located in the Grid Definition panel.
  4. Click Apply to accept your changes and to keep the Properties Browser open.

Specifying the coverage assets

Assets properties enable you to specify the STK objects used to provide coverage. In this case, you want to use all of the satellites in the Satellite Collection. For all Satellite Collection objects, the STK application automatically generates a subset named AllSatellites that contains all members of the collection. Assign this subset to your Coverage Definition object.

  1. Select the Basic - Assets page.
  2. Expand () Walker_Collection () in the Assets list.
  3. Select the AllSatellites () Satellite Collection subset.
  4. Click Assign.
  5. Click Apply to accept your changes and to keep the Properties Browser open.

Clearing Automatically Recompute Accesses

The STK application automatically recomputes accesses every time you update an asset on which the coverage definition depends, such as your Satellite Collection object. If you want to control when the STK software computes coverage, you need to turn this option off in the Coverage Definition object's Advanced properties page.

  1. Select the Basic - Advanced page.
  2. Clear the Automatically Recompute Accesses check box.
  3. Click OK to accept your changes and to close the Properties Browser.
  4. Rename CoverageDefinition1 () CoverageDefinition.

Using the Compute Accesses tool

The ultimate goal of coverage is to analyze accesses to an area by using assigned assets and applying necessary limitations upon those accesses. Compute coverage with the Compute Accesses tool.

  1. Right-click on CoverageDefinition () in the Object Browser.
  2. Select CoverageDefinition in the shortcut menu.
  3. Select Compute Accesses in the CoverageDefinition submenu.

Generating a Percent Coverage graph

Now that you have set up and computed the coverage analysis, you can examine the quality of the coverage. But before you do that, take a quick look at the quality of the system you set up. One way to do that is to generate a Percent Coverage graph. This graph tells you how well the satellite in the Walker Collection is able to cover the Earth throughout the scenario time period.

  1. Select the Analysis menu.
  2. Select Report & Graph Manager... ().
  3. Open the Object Type drop-down list when the Report & Graph Manager opens.
  4. Select CoverageDefinition.
  5. Select CoverageDefinition () in the Object Type list.
  6. Select the Percent Coverage () graph in the Installed Styles () folder inside the Styles panel.
  7. Click Generate. . ..

    8. Percent Coverage graph

    Take a look at how the current coverage stays low throughout the analysis period, but how the accumulated coverage increases over time. This gives you an idea of how well a single satellite can cover the region. You can understand this further with a Figure of Merit object.

  8. Close the Percent Coverage graph and the Report & Graph Manager.

Designing the coverage definition Figures of Merit

You set up the problem using a Coverage Definition object. The STK software enables you to specify the method by which the quality of coverage is measured using a Figure Of Merit object. You can attach FOM objects to a Coverage Definition object; they provide the means for evaluating the quality of coverage provided by Coverage Definition's assigned objects (or assets).

In this study, you will focus on two parameters: the Number of Assets (N Asset Coverage) and the Revisit Time. The mission requirements state you must have at least two assets covering every grid point at all times.

Inserting an N Asset Figure of Merit object

An N Asset FOM determines how many different assets are simultaneously covering each individual grid point at each time in the analysis period.

You can specify that the FOM compute the minimum value from the set of all grid points to make sure all grid points are at or above that threshold.

  1. Insert a Figure of Merit () object using the Define Properties () method.
  2. Select CoverageDefinition () in the Object Tree when the Select Object dialog box opens.
  3. Click OK to confirm your selection and to close the Select Object dialog box.

Setting the N Asset coverage definition

You want to measure if at least two satellites simultaneously cover every single point in the coverage analysis.

  1. Select the Basic - Definition page when the Properties Browser opens.
  2. Open the Type drop-down list in the Definition panel.
  3. Select N Asset Coverage.
  4. Open the Compute drop-down list.
  5. Select Minimum.

Using Minimum calculates the minimum number of assets available over the entire coverage interval.

Selecting the N Asset FOM satisfaction criterion

You can restrict the FOM's behavior so that the STK application only applies the graphical properties of the FOM when a chosen satisfaction criterion is met.

  1. Select the Enable check box in the Satisfaction panel.
  2. Open the Satisfied if drop-down list.
  3. Select At Least.
  4. Enter 2 in the Threshold field.

    5. Satisfaction is achieved when the FOM value is greater than or equal to the Threshold.

  5. Click OK to accept your changes and to close the Properties Browser.
  6. Rename FigureofMerit1 () NAsset.

Inserting the revisit time Figure of Merit object

Now that the coverage has a threshold of at least two satellites per grid point, you can set up a new figure of merit for the revisit or gap time.

  1. Insert a Figure of Merit () object using the Define Properties () method.
  2. Select CoverageDefinition () in the Object Tree when the Select Object dialog box opens.
  3. Click OK to confirm your selection and to close the Select Object dialog box.

Defining the revisit time coverage definition

Revisit time (gap time) measures the intervals during which coverage is not provided. You want to minimize the gap time so that the maximum value satisfies the requirements with a zero-second gap time.

  1. Select the Basic - Definition page when the Properties Browser opens.
  2. Open the Type drop-down list in the Definition panel.
  3. Select Revisit Time.
  4. Enter 2 in the Min # Assets field.

    5. Min # Assets specifies the minimum number of simultaneous assets that are required for coverage.

  5. Keep the Compute and End Gaps options set as their default selections.

Compute - Maximum specifies that the computed value is the duration of the longest gap in coverage over the entire coverage interval. Setting the End Gaps to Include has gaps at the ends of the analysis interval included in your revisit time computations.

Selecting the revisit time FOM satisfaction criteria

You will use the At Most Satisfaction Criteria. Using At Most, the FOM value is less than or equal to the Threshold value.

  1. Select the Enable check box in the Satisfaction panel.
  2. Open the Satisfied if drop-down list.
  3. Select At Most.
  4. Leave the default Threshold value of 0 sec.
  5. Click OK to accept your changes and to close the Properties Browser.
  6. Rename FigureofMerit2 () RevisitTime.

At this point, you might be wondering why you're setting up both FOMs to use a minimum of two satellites when you currently have one satellite in your collection. When you use the ModelCenter software, you will set it up so that there are six orbital planes with six satellites per plane.

Closing out of the STK application

With your baseline scenario configured, save your scenario and close out of the STK application in preparation for the next step.

  1. Save () your scenario.
  2. Close any open reports, the Report & Graph Manager, and any open tools.
  3. Close the STK application.

Creating a new ModelCenter project

The Ansys ModelCenter software is designed for multidisciplinary analysis and design optimization. It allows you to automate complex workflows, integrate multiple engineering tools, and optimize designs within model-based systems engineering frameworks. By wrapping analysis programs like the STK software and running them in an automated fashion, the ModelCenter software makes the design process more efficient, saves engineering time, and reduces the chances for error in the design process.

  1. Open the ModelCenter () application.
  2. Click Start a New Model in the Welcome to ModelCenter dialog box.
  3. Click Process when the What type of model would you like to create? dialog box opens.
  4. Navigate to your scenario folder (for example, C:\Users\<username>\Documents\STK_ODTK 13\ImagingConstellation.
  5. Enter ImagingConstellation in the File name field.
  6. Ensure the Save as type is set to the ModelCenter Model (Zip) (*.pxcz).
  7. Click Save.

Using the STK Plugin for ModelCenter

The STK Plugin for ModelCenter imports a copy of the desired Scenario and opens it in an instance of the STK application. Launch the plugin by adding it to your workflow's analysis view from the Server Browser.

  1. Select favorites () in the Server Browser at the bottom of the window.
  2. Click and drag the STK component () into the dashed circle underneath "Drop items here to build the model" in the workflow's Analysis View.
  3. Select ImagingConstellation.sc when the Open STK Scenario file dialog box opens.
  4. Click Open.
  5. After a few moments, the STK Analyzer window will open.

The ImagingConstellation scenario file will open in the STK application in the background.

Setting up your analysis with Analyzer

You are now ready to dive into some trade study analysis using the ModelCenter software. You can build a simple example and then load the results into a more complex study. The goal is to become familiar with the Analyzer workflow in the ModelCenter application, as well as loading results of previously run analyses.

Selecting the input variables

Use the STK Analyzer window to configure the input and output variables available for further analysis with the Analyzer capability. You must first select an object in the STK Variables tree on the left. When you select an object, all possible input variable candidates for that object are listed under the General tab and the Active Constraints tab in the STK Property Variables panel.

  1. Select Walker_Collection () in the STK Variables tree.
  2. Select the Walker () property in the STK Property Variables tree.
  3. Move () Walker () to the Analyzer Variables list.

Note that your Walker constellation's orbital parameters, including the Argument of Periapsis, Eccentricity, Inclination, Planes, RAAN, and more have all be added as Inputs in the Analyzer Variables list.

Defining the output variables

Now that the input variables are defined, you can add the output variables. The output variables are the variables you'd like to solve for. You want to solve for Minimum N Asset Overall and Maximum Revisit Time Overall. The same data providers that are available in the Report & Graph Manager in the STK application are available in the Data Provider Variables tree.

  1. Expand () CoverageDefinition () in the STK Variables tree.
  2. Select NAsset ().
  3. Expand () the Overall Value () data provider in the Data Provider Variables tree.
  4. Select the Minimum () data provider element.
  5. Move () Minimum () to the Analyzer Variables list.
  6. Select RevisitTime () in the STK Variables tree.
  7. Expand () the Overall Value () data provider.
  8. Select the Maximum () data provider element.
  9. Move () Maximum () to the Analyzer Variables list.

    10. Note that both FOM values have been added as Outputs in the Analyzer Variables list.

  10. Click OK to accept your changes and to close the STK Analyzer window.

    11. This will also close the STK application, which had been running in the background.

Using the Parametric Study tool

The Parametric Study tool runs a model through a sweep of values for some input variable. The resulting data can be plotted to view trends.

Specifying the variables

To perform a Parametric Study, one design variable and one or more responses must be specified. For the design variable, a starting value, an ending value, and the number of steps must be specified.

  1. Expand () all the elements in the Component Tree.
  2. Click Parametric Study () in the Standard toolbar.
  3. Click and drag SemiMajorAxis () from the Component Tree to the Design Variable field when the Parametric Study tool opens.
  4. Set the following Design Variable values:
    5. Option Value
    starting value 6880
    ending value 7680
    step size 100

    Note the number of samples is automatically set to 9. These settings will vary the semi-major axis in 100-kilometer increments. It will take a total of nine runs to complete the trade study.

  5. Click and drag NAsset - Overall_Value - Minimum () and RevisitTime - Overall_Value - Maximum () from the Component Tree to the Responses list:

Defining the Walker variables

Define the walker parameters within the parametric study.

  1. Locate the Walker - Shell_Walker_Group list, located in the Component Tree. To the right of each variable is a value that you can click to change the value.
  2. Set the following options for Walker_Constellation:
    3. Name Value
    Planes 6
    SatellitesInPlanes 6

Running the parametric trade study

This parametric trade study will take a few minutes to run.

  1. Click Run....

    2. Clicking Run... will open the Data Explorer, which is a tool used by Trade Study tools to display data collected from a Model. While data are being collected, the Data Explorer displays a progress meter, a halt button, and the data. In each of the runs, you should see the revisit time (gaps) decrease as the semi-major axis increases. Eventually, it goes to zero. The average increases to two for the number of assets. The minimum number of assets eventually reaches two.

  2. Close the 2D Scatter Plot that opened when the trade study finished running.

Generating a 3D Scatter Plot

There are a few ways to view the data. One interactive way to view the data is with a 3D Scatter Plot. A 3D Scatter Plot displays an x-y plot of variables in the model.

  1. Bring the Table page to the front when all runs finish.
  2. Click Add View () on the Table page toolbar.
  3. Select 3D Scatter Plot () in the drop-down menu.

Modifying the 3D Scatter Plot

Use the Plot Options menu to change which variable is displayed on which axis.

  1. Click Dimensions in the Plot Options menu when the 3D Scatter Plot opens.
  2. Set the following options:
    3. Option Value
    x Maximum
    y Minimum
    z SemiMajorAxis
  3. Click anywhere on the graph to close the Plot Options menu.

Reviewing the 3D Scatter Plot

Examine the 3D Scatter Plot.

  1. Hover over any design point to get information about that run.

    2. ModelCenter 3D Scatter plot

    Note the semi-major axis of the last run (7,680 km). This gives you the requirements you are looking for: 2 assets with a 0-second revisit time.

  2. Close the 3D Scatter Plot and the Table page when you are finished.
  3. Click No when prompted to close your trade study without saving.
  4. Close the Parametric Study tool.

Saving the results of your parametric study

All of the criteria meet in the final run, whose semi-major axis is 7,680 km; however, remember that the semi-major axis values are raised in 100-kilometer increments. There is likely a minimum semi-major axis that enables you to achieve your goals sooner. If you consider cost, which might be tied to a higher orbit, you can find a lower semi-major axis that also reduces cost.

Push the results of a single run to the STK application and examine the scenario.

  1. Enter 7680 as the Value for the SemiMajorAxis input variable in the Component Tree.

    2. You do not need to enter units.

  2. Click Save () to save your ModelCenter workflow.
  3. Keep the ModelCenter application open.

Updating your STK scenario

Update your Walker Collection with the data from the last run in your trade study.

  1. Reopen the STK application ().
  2. Reopen your ImagingConstellation scenario.
  3. Open Walker_Collections' () Properties ().
  4. Select the Walker Group row in the Walker Properties panel.
  5. Click Edit selected shell () in the Shells toolbar.
  6. Set the following options in the Shell Properties panel when the Edit Shell dialog box opens:
    7. Name Value
    Planes 6
    SatellitesInPlanes 6
  7. Set Semi-Major Axis (a) to 7680 km.
  8. Click Save Changes to confirm your changes and to close the Edit Shell dialog box.
  9. Click OK to confirm your changes and to close the Properties Browser.

Recomputing the accesses

With your Walker Satellite Collection updated, recompute the accesses.

  1. Right-click on CoverageDefinition () in the Object Browser.
  2. Select CoverageDefinition in the shortcut menu.
  3. Select Compute Accesses in the CoverageDefinition submenu.

Examining the data

Now that you have a result loaded in, look at some of the reports and graphs in the STK application that can shed some light on the scenario.

Generating a Percent Satisfied report

A Percent Satisfied report reports coverage properties, figure of merit properties, and the amount of the coverage analysis grid which satisfies the satisfaction criteria defined in the figure of merit based on the static definition of the figure of merit.

  1. Right-click on NAsset () in the Object Browser.
  2. Select Report & Graph Manager... () in the shortcut menu.
  3. Select the Percent Satisfied () report in the Installed Styles () folder when the Report & Graph Manager opens.
  4. Click Generate. . ..
  5. Scroll to the bottom of the report and look at the % Satisfied column.

    6. You should have 100% satisfaction, which means you have a minimum of two satellites with access to every point in the coverage grid. The Percent Satisfied report confirms that information.

  6. Close the Percent Satisfied report.

Generating a Grids Stats Over Time report

A Grid Stats Over Time report reports coverage properties, figure of merit properties, and statistical information on figure of merit values, sampled over all grid points, over time. Grid directions for which a value cannot be computed are not included in the reported statistics.

  1. Select the Grids Stats Over Time () report in the Installed Styles () folder.
  2. Click Generate. . ..
  3. Scroll through the report.

    4. You can see that you meet the minimum, but you have a few locations that have up to five or six satellites with access (depending on the analysis period). This creates a lot of redundancies, so you can start thinking of optimizing the setup.

    You have two options at this point:

    • Continue to test configurations using parametric scans, carpet studies, and design of experiments.
    • Optimize the scenario to find the optimal semi-major axis.

    You may also consider if you need to change other factors with the study, such as number of satellites or planes.

Closing out of the STK application

With your scenario reconfigured, save your scenario and close out of the STK application in preparation for the next step.

  1. Close any open reports and the Report & Graph Manager when finished.
  2. Save () your scenario.
  3. Close any open reports, the Report & Graph Manager, and any open tools.
  4. Close the STK application.

Loading a precomputed optimization trade study

The study you will load in was run for approximately an hour using the Satellite Collection object. Older versions of the STK software required the use of the Walker Tool and individual Satellite objects, which took upwards of 10 hours to analyze. The goal is to minimize the semi-major axis and the total number of satellites. At the same time, you want to minimize the revisit time (no gaps) and have two satellites maintain access with a point on the ground.

Opening the precomputed trade study

Load in the data from the precomputed trade study and examine it.

  1. Return to the ModelCenter application.
  2. Click Open () on the Standard Toolbar.
  3. Browse to the location of the precomputed trade study you extracted earlier (for example, C:\Users\<username>\Documents\STK_ODTK 13\ImagingConstellation).
  4. Select DME_OptStudy3.tstudy ().
  5. Click Open.

This opens the Optimization tool, a 3D Scatter Plot, and the trade study's Table page.

Understanding the results

View the results in the precomputed trade study's 3D Scatter Plot.

  1. Bring the 3D Scatter Plot window to the front.
  2. Examine the 3D Scatter Plot.

    3. You can see the configurations that met the criteria in blue and those that didn't in gray.

    ModelCenter Optimization tool 3D Scatter plot

  3. Hover over any design point in the graph to see more information about a run.
  4. Select the feasible design point with the lowest semi-major axis.

    5. This is the lowest semi-major axis that satisfies all of your criteria, which, for this trade study, was design point 278, with a semi-major axis of 7637.6 km.

  5. Bring the Data Explorer window to the front.
  6. Examine the runs on the Table page.

    7. You can scroll to see all the runs that were conducted and each result. You also have the option to export the data into Excel or another tool for post-processing.

  7. Scroll to run 278.

    8. Table View showing best run

    This is the run that best met all of the criteria of the trade study.

If you want to run the trade study yourself, proceed to the Performing an Optimization Study section. Otherwise, skip to Saving your model section.

Performing an Optimization Study

Looking at the data, there is a clear point that meets all the conditions for the study. Use the STK Analyzer Optimization capability, by means of the ModelCenter software's Optimization tool, to get an idea of the workflow. The Optimization tool is a collection of optimization algorithms that you can use within the ModelCenter application. A common graphical user interface (GUI) is provided to define optimization problems. An algorithm selection wizard is also provided to make it easy to choose algorithms that will work best for the problem at hand.

This is an additional section for users who would like to set up an optimization themselves.

Closing out your trade study

Close out the precomputed trade study.

  1. Close the 3D Scatter Plot.
  2. Close the Data Explorer window.
  3. Close the Optimization tool.

Adding an additional output variable

You want to make sure you maintain 100% coverage satisfaction across your area of interest with your optimized solution. Add the NAsset Figure of Merit's Percent Satisfied output variable to use as an objective in your optimization study.

  1. Right-click on the STK_ODTK13 component in the Analysis View.
  2. Select Show Component's GUI () in the shortcut menu.
  3. Expand () CoverageDefinition () in the STK Variables tree when the STK Analyzer window opens.
  4. Select NAsset ().
  5. Expand () the Static Satisfaction () data provider.
  6. Select the Percent Satisfied () data provider element.
  7. Move () Percent Satisfied () to the Analyzer Variables list.
  8. Click OK to accept your changes and to close the STK Analyzer window.

Defining the optimization objective

To perform an Optimization Study, an objective function and a least one design variable must be specified. The objective functions can be specific variables or equations composed of multiple output variables. For each objective, you must specify whether you want to minimize or maximize the objective or find a design where the objective has as specific value. Your current objective is to minimize the semi-major axis while meeting the coverage criteria.

  1. Click Optimization Tool () on the Standard Toolbar.
  2. Expand () all components in the Component Tree.
  3. Click and drag SemiMajorAxis () from the Component Tree to the Objective field when the Optimization tool opens.
  4. Ensure the Goal is set to minimize.
  5. Click and drag Percent_Satisfied () from the Component Tree to the Objective field.
  6. Open the Goal drop-down menu () for Percent_Satisfied.
  7. Select maximize.

    8. You want to ensure that your solution maximizes the coverage at 100% to conclusively rule out any combinations that provide less than full coverage.

Defining the constraints

Constraints restrict particular variables to a region or value, that is, a bound specified in the list of constraints prevents a design point from being found that causes that output variable to occur outside the specified region. For this optimization, you want to minimize the number of satellites that will provide coverage without any gaps.

  1. Click and drag NAsset - Overall_Value - Minimum () from the Component Tree to the Constraint field.
  2. Set the Lower Bound to 2.
  3. Leave the Upper Bound blank.
  4. Click and drag Revisit Time - Overall_Value - Maximum () from the Component Tree to the Constraint field.
  5. Set the Lower and Upper Bounds to 0.

Each constraint must have either an upper or lower bound, but can also have both. Constraints can also be equations composed of multiple variables.

Defining the SemiMajorAxis design variable

The design variables are the variables that the optimizer will modify to meet the objective. You must enter the bounds between which the optimizer is allowed to set the design variables. For continuous variables, like the semi-major axis, these bounds are required.

  1. Click and drag SemiMajorAxis () from the Component Tree to the Design Variable field.
  2. Set the following Lower and Upper bounds:
    3. Option Value
    Lower Bound 7580
    Upper Bound 7680

Defining the number of satellites per plane

Optimize for the number of satellites per plane. Both the start and end values must be specified for the number of satellites, which is defined by an integer value. The start and end values are used to create the enumeration for the integer; all integer values between the start and end values are used.

  1. Click and drag SatellitesInPlanes () from the Component Tree to Design Variable field.
  2. Set the following options in the dialog box:
    3. Option Value
    Start Value 3
    End Value 6
  3. Click OK to confirm your selection and to close the dialog box.

Defining the number of planes

Like the SatellitesInPlanes variable, the number of planes is also an integer value.

  1. Click and drag Planes () from the Component Tree to the Design Variable field.
  2. Set the following options in the dialog box:
    3. Option Value
    Start Value 3
    End Value 6
  3. Click OK to confirm your selection and to close the dialog box.

Selecting an algorithm

There are over 30 algorithms to choose from when using the Optimization tool, including gradient-based optimizers, genetic algorithms, multiobjective algorithms, and other heuristic search methods. For this trade study, you will use the Darwin algorithm.

  1. Open the Algorithm drop-down list.
  2. Select Darwin Algorithm.

    3. Darwin is a genetic search algorithm developed specifically for solving engineering optimization problems. It is capable of handling discrete variables, continuous variables, and any number of constraints. Because Darwin does not require gradient information, it is able to effectively search non-linear and noisy design spaces. A penalty function is used to handle violated constraints. It uses elitist method to keep the best design(s) from the previous generation When more than one objective is defined, Darwin will search for a series of best designs (Pareto set) union non-dominated design search.

  3. Click Run.

Be patient. Your trade study could take one or two hours to run.

Reviewing the optimized results

Review the Optimization tool output.

Your values may be different than those below.

  1. When the trade study is finished, bring the Optimization tool to the front.
  2. Click View Output..., located in the lower-right corner of the Optimization tool.
  3. Select the Best Design tab when the Optimization tool Results window opens.

    4. Best Design

    You should get similar results to those of the precomputed trade study. Your best design run number may be different from the image. That's OK. At the top of the Optimization tool Results window, it will tell you the best design run number. All the values on the right of the window show you the best values.

  4. Bring the Table page to the front.
  5. Scroll to the column with the same run number as the best design.
  6. This data will be the same as the values seen in the Optimization tool Results - Best Design tab.
  7. Note the value for SemiMajorAxis has been reduced to 7637.6 km while maintaining 100% satisfaction.

Saving your model

Save your work and close out ModelCenter application.

  1. Close out any open plots, tools, and the Data Explorer window.
  2. Click No when prompted to close your trade study without saving.
  3. Click Save () to save your ModelCenter workflow.
  4. Close the ModelCenter application.

Updating your STK scenario

Update your Walker Collection with the data from the last run in your trade study.

  1. Reopen the STK application ().
  2. Reopen the ImagingConstellation scenario.
  3. Open Walker_Collections' () Properties ().
  4. Select the Walker Group row in the Walker Properties panel.
  5. Click Edit selected shell () in the Shells toolbar.
  6. Set the Plane1 : Slot 1 Semi-Major Axis (a) to 7637.6 km when the Edit Shell dialog box opens.
  7. Click Save Changes to confirm your changes and to close the Edit Shell dialog box.
  8. Click OK to confirm your changes and to close the Properties Browser.

Recomputing the accesses

With your Walker Satellite Collection updated, recompute the accesses.

  1. Right-click on CoverageDefinition () in the Object Browser.
  2. Select CoverageDefinition in the shortcut menu.
  3. Select Compute Accesses in the CoverageDefinition submenu.

Examining the data

Now that you have a result loaded in, regenerate the Percent Satisfied report.

  1. Right-click on NAsset () in the Object Browser.
  2. Select Report & Graph Manager... () in the shortcut menu.
  3. Select the Percent Satisfied () report in the Installed Styles () folder when the Report & Graph Manager opens.
  4. ClickGenerate. . ..
  5. Scroll to the bottom of the report.

    6. You know from the results of the trade study that this configuration enables you to have a minimum of two satellites with access to a point on the ground. This report confirms that you have 100% satisfaction.

  6. Close the Percent Satisfied report.

Graphing the results

Create a Grid Stats Over Time graph to evaluate your optimization. A Grid Stats Over Time graph is a plot of the minimum, maximum, and average figure of merit values, sampled over all grid directions, over time.

  1. Return to the Report & Graph Manager.
  2. Select the Specify Time Properties option in the Time Properties panel.
  3. Select the Use step size / time bound option.
  4. Enter 1 sec in the Step size field.

    5. By reducing the step size to one second, the graph will show more information.

  5. Select the Grid Stats Over Time () graph in the Installed Styles () folder.
  6. Click Generate. . ..

Grid stats over time graph

From these data, you can see that you have full coverage throughout your mission. The minimum criterion of two satellites with simultaneous access to a grid point is met. This is confirmed in the Percent Satisfied Report and the Grid Stats Over Time graph. You can also see that you have a maximum of four to six satellites with simultaneous access to a grid point. This redundancy is key, in case you should lose a satellite in the course of a mission.

Your objective to create a new satellite constellation that provides persistent, stereo coverage of hypersonic vehicles across the world has been met.

Saving your work

Clean up your workspace and close out your scenario.

  1. When finished, close all tools, graphs and reports you still have open.
  2. Save () your work.
  3. Close the STK application.

Summary

You have the results of the optimization run, but there are many parameters that you can vary in the analysis. The flexibility of both the STK and the ModelCenter software enable you to change an aspect of the mission (like the semi-major axis) while knowing that it carries through and is used in all calculations. You can link your analysis into many other aspects of your model, incorporating cost breakdowns, the total number of satellites, and other parameters from many different, linked sources. You can thus integrate the mission earlier and take into consideration all of the factors in the mission environment.

DME Lesson 2: Hypersonics and EOIR

The next lesson in the DME series focuses on Hypersonics and EOIR. You will use a starter scenario and build your own hypersonic vehicle. You will use an EOIR sensor to image it. This leads up to sessions three and four of the DME series where you bring the constellation from this lesson and the flight from session two together to understand how all components for the mission works together.