Optimizing a Satellite's Orbit with ModelCenter

STK Premium (Air), 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.

Required product install: The Ansys ModelCenter® model-based systems engineering software and the STK Plugin for ModelCenter are required to complete this tutorial. The ModelCenter software is available through the Ansys Universal Installer and the STK Plugin for ModelCenter is included with the STK Premium installation. Contact AGI support for installation help.

ModelCenter installation prerequisites: The ModelCenter software installs the current version of Java and Python supported by Ansys, but you can also use your own versions. See the Installation instructions in the ModelCenter Installation Guide and Supported Versions documentation for more information. Contact AGI support for help with installation.

This tutorial was written using version 2026 R1 of the Ansys ModelCenter® model-based systems engineering software. Refer to the ModelCenter Supported Versions page in the ModelCenter Installation Guide and Supported Versions documentation for compatibility information.

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

Engineers and operators require a quick way to determine how various orbital parameters will affect the ability of a sensor or a camera to view the surface of the Earth. Your team wants to launch a satellite into low Earth orbit (LEO) to monitor the extent of Arctic sea ice. Data will be relayed through satellite in a geosynchronous orbit (GEO) back to a ground processing facility in Montreal. You want to understand what the effects of changing the satellite's orbital parameters and the configuration of its onboard sensor will have on its ability to view the polar ice cap.

Solution

Use the STK software's Coverage capability and the Analyzer capability, which is part of the Ansys ModelCenter® model-based systems engineering software, to perform a series of trade studies to better understand how the LEO satellite's orbit and sensor parameters impact coverage. Then, use the STK Analyzer Optimization capability to optimally configure the sensor to maximize the extent of coverage over the Arctic ice pack.

What you will learn

Upon completion of this tutorial, you will understand how to:

  • Parametrically explore the design space in order to optimize your mission
  • Perform parameter studies that vary an input variable through a range of values
  • Plot one or more output variables
  • Analyze an STK scenario for trends
  • Generate 3D surface plots and perform optimization studies
  • Optimize scenario parameters to meet mission objectives

Using the starter scenario

To speed things up and allow you to focus on the portion of this exercise that teaches you how to use the ModelCenter software, a partially created scenario has been provided for you.

Opening the starter scenario

The starter scenario is included in your install.

  1. Launch the STK application ().
  2. Click Open a Scenario in the Welcome to STK dialog box.
  3. Browse to <Install Dir>\Data\Resources\stktraining\VDFs.
  4. Select SensorOpt.vdf.
  5. Click Open.

Saving the VDF as a scenario file

Save and extract the VDF data in the form of a scenario folder. When you save a VDF in the STK application, it will save in its originating format. That is, if you open a VDF, the default save format will be a VDF (.vdf). If you want to save and extract a VDF as a scenario folder, you must change the file format by using the Save As feature. This will create a permanent scenario file complete with child objects and any additional files packaged with the VDF.

  1. Open the File menu when the starter scenario opens.
  2. Select Save As....
  3. Select the STK User folder in the navigation pane when the Save As dialog box opens.
  4. Select the SensorOpt folder.

    5. A scenario folder with the same name as the VDF was created for you when you opened the VDF in the STK application. This folder contains the temporarily unpacked files from the VDF.

  5. Click Open.
  6. Open the Save as type drop-down list.
  7. Select Scenario Files (*.sc).
  8. Select the SensorOpt scenario file in the file browser.
  9. Click Save.
  10. Click Yes when the Confirm Save As Dialog box opens to overwrite the existing scenario file in the folder and to save your scenario.

When saving a VDF as a scenario folder, you should extract its contents to the scenario folder the STK application automatically creates for you in the STK User folder. See the Permanently Extracting a VDF as a Scenario Folder and VDF Setup Considerations pages for more information.

Save () often during this lesson!

Reviewing the starter scenario

The starter scenario consists of your satellite of interest, LEO, which has an attached simple conic sensor, Ice_Finder. The sensor has a Ground Sample Distance (GSD) constraint of five meters, as you want to be able to resolve icebergs as small as five meters in diameter. The Arctic region you are studying is represented by a Coverage Definition object, Arctic_Monitor. Arctic_Monitor's grid area of interest is the Area Target object named Arctic; the grid is constrained by a Facility object, Seed, which is not displayed in the 3D Graphics window, and the quality of coverage is gauged by a Figure Of Merit object, CoveragePerDay. Arctic_Monitor's assigned asset is Relay_Chain, a Chain object. Animate the scenario to view the Chain object's links from the ground station in Montreal through the GEO_Relay to LEO and LEO's Ice_Finder sensor.

  1. Click Start () in the Animation toolbar to animate the scenario.
  2. Watch LEO () as it scans the polar ice cap.
  3. Click Reset () when you are finished.

    4. LEO viewing polar ice cap

Using the Coverage capability for analysis

The STK software's Coverage capability allows you to analyze the global or regional coverage provided by one or more assets (facilities, vehicles, sensors, etc.) while considering all accesses. To address area coverage capabilities, Coverage provides you with two STK object classes: Coverage Definition objects and Figure of Merit objects. Before performing a coverage analysis, however, you must first compute the accesses for your Coverage Definition object.

Using the Compute Accesses tool

The ultimate goal of the STK software's Coverage capability is to analyze accesses to an area using assigned assets and applying necessary limitations upon those accesses. Compute coverage with the Compute Accesses tool.

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

Generating a Grid Stats report

The scenario has a seven-day analysis period. Coverage is evaluated with a Figure of Merit object, CoveragePerDay. CoveragePerDay's definition is set to Coverage Time and its compute option is Per Day. Per Day is the total coverage time divided by the number of days in the coverage interval. You will use the ModelCenter software to perform trade studies on CoveragePerDay's Grid Stats. First, manually examine data from the STK application by generating a Grid Stats report to see the smallest and largest total number of accesses for the points in the grid.

  1. Right-click on CoveragePerDay () in the Object Browser.
  2. Select Report & Graph Manager... () in the shortcut menu.
  3. Select the Grid Stats () report in the Installed Styles () folder in the Styles panel when the Report & Graph Manager opens.
  4. Click Generate....
  5. Note the Minimum, Maximum, and Average values in the report. These values will be accessible in Analyzer as output variables.

    6. Grid Stats Report

    This report indicates that for all the grid points defining the polar cap, at least one point is not seen by the satellite (that is, the Minimum value in seconds is 0.000), at least one point is seen for approximately 663 seconds, and, on average, points are seen for approximately 219 seconds per day during your analysis period.

  6. Close the Grid Stats report when you are finished.
  7. Click Close to close the Report & Graph Manager.

Saving your STK scenario

Before opening the ModelCenter application, save your scenario to save the accesses you computed and close out of the STK application.

  1. Save () your scenario.
  2. 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.

  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\SensorOpt).
  5. Enter SensorOpt in the File name field.
  6. Ensure the Save as type is set to the ModelCenter Model (Zip) (*.pxcz).
  7. Click Save.

Launching 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 ModelCenter 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 SensorOpt.sc when the Open STK Scenario file dialog box opens.
  4. Click Open.

    5. This will open the STK scenario and STK Analyzer windows. Please be patient.

The SensorOpt scenario file will open in the STK application in the background. If the STK application opens in front of ModelCenter, bring the ModelCenter application window back to the front.

Setting up your analysis with Analyzer

Use the STK Analyzer window to configure the input and output variables available for further analysis with the Analyzer capability. You can add almost any STK variable as ModelCenter input or output variables. If you change the value of a variable in your scenario through the STK interface or the ModelCenter Component Tree, you should re-add the variable into ModelCenter or re-run the workflow before running any trade studies with the new value.

Selecting the Analyzer input variables

Your first study will focus on several of the satellite's orbital parameters, such as Inclination, RAAN, and the Semi-major Axis, as input variables. Before you can use them in your model, however, you must first add them to your design space.

  1. Select LEO () in the STK Variables tree.

    2. When you select an object in the STK Variables tree, 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.

  2. Expand () the Propagator (J4Perturbation) () property in the STK Property Variables tree.
  3. Move () the following input variables () to the Analyzer Variables list:
    • SemiMajorAxis
    • Inclination
    • RAAN

Note that all three variables are listed as Inputs in the Analyzer Variables list.

Selecting the output variables

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 () Arctic_Monitor () in the STK Variables tree.
  2. Select CoververagePerDay ().
  3. Expand () the Overall Value () data provider in the Data Provider Variables tree.
  4. Move () the following data provider elements () to the Analyzer Variables list:
    • Minimum
    • Maximum
    • Average

    Note that the variables are listed as Outputs in the Analyzer Variables list.

  5. Click OK to confirm your selections and to close the STK Analyzer window.

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

Analyzing the impact of inclination on coverage

You want to understand how LEO's inclination affects its ability to monitor the Arctic region. Create a Parametric Study to plot the inclination against the coverage time per day.

Creating a benchmark

You can quickly analyze your current setup, which will create a benchmark of the output variable values.

  1. Expand () all the components in the Component Tree.

    2. expanded component tree

  2. Note the input variable values in the Component Tree.

    3. These are the values imported into ModelCenter from the SensorOpt scenario.

  3. Click Run () on the Standard toolbar.
  4. When completed, note the output variable values have been computed.

The output variable values are based on the default input variables. Overall, you want an increase to the overall output variables. You can see that these values match the values from the Grid Stats report you created earlier.

Using the Parametric Study tool

The Parametric Study tool runs a workflow through a sweep of values for some input variable. You can plot the resulting data to view trends.

  1. Click Parametric Study () on the Standard toolbar.
  2. Click and drag the Inclination () input variable from the Component Tree to the Design Variable field when the Parametric Study tool opens.
  3. Set the following Design Variable values:
    4. Option Value
    starting value 45
    ending value 135
    step size 10
  4. Click and drag Minimum (), Maximum (), and Average () output variables from the Component Tree to the Responses field.
  5. Click Run.

Clicking Run will open the Data Explorer, which is a tool used by Trade Study tools to display data while they are being collected from your Model. While data are being collected, the Data Explorer displays a progress meter, a halt button, and the data. The Table page of the Data Explorer displays trade study data in a tabular form. It is the default window that is present for all trade studies. Cells are shaded differently depending on the associated variable's state. Input variables are shown with green text, valid values are displayed with black text, invalid values are displayed with gray text, and modified values are displayed with blue text. From the table it is possible to view and edit all values in your trade study and even to add and remove whole runs.

Creating a 2D Line Plot

Once the trade study is complete and all data have been collected, the Data Explorer toolbar becomes active. The Data Explorer stores values for all variables in a workflow and special variables from the trade study. Some trade study tools will automatically launch a default plot window when the trade study runs. For other plots, you can create them from the Add View menu. For this study, you will create a 2D Line Plot. A 2D Line Plot displays an X-Y plot for variables in your model. Any variable in the workflow can be plotted against any other variable.

  1. Bring the Data Explorer window to the front when the when the trade study is finished running.
  2. Click Add View () on the Data Explorer toolbar.
  3. Select 2D Line Plot () in the drop-down menu.

Setting the plot variables

The plot shows the minimum coverage time versus the inclination. You could change the plot's y dimension to maximum or average to adjust the plot as needed. Instead, you will add the maximum and average coverage results to the plot for comparison on one plot. Use the Plot Options menu to set which variable is displayed on which axis. In certain plots, you can set other global plot controls based on the plot variables. In this case, you want to view several variables: the minimum, maximum, and average power. Minimum will be Series 1, Maximum will be Series 2, and Average will be Series 3.

  1. Click Dimensions () in the Plot Options menu on the left-hand side of the 2D Line Plot.
  2. Click Add Series (+) when the Dimensions dialog box opens.

    3. This creates Series 2.

  3. Open the x drop-down list.
  4. Select Inclination.
  5. Open the y drop-down list.
  6. Select Maximum.

    7. This adds the Maximum inclination values to the plot.

  7. Click Add Series (+).

    8. This creates Series 3.

  8. Set x to Inclination.
  9. Set y to Average.

    10. This adds the Average inclination values to the plot.

  10. Click on the plot to close the Plot Options menu.

Reviewing the 2D Line Plot

With your three series configured, review your plot.

  1. Review the plot.

    2. Minimum, Maximum, and average seconds vs. Inclination

  2. Hover your cursor over a data point in the plot.

    3. This will show you information about that point in a Design Tooltip.

  3. Click the Open Design View ellipsis in the lower-right corner of the Design Tooltip to open the Design View dialog box.

    4. This provides more detailed information of the selected point.

  4. Close the Design View dialog box.

Results from the first study are as expected: the closer the inclination is to 90 degrees, the better your coverage will be. This makes sense, as the ice cap covers the North Pole and your coverage will be best when your orbit takes you through the rotational center point of the area you are trying to cover.

There is an additional interesting trend on the plot: the highest maximum, average and minimum coverage falls somewhere between 85 and 95 degrees. These values can help you narrow your design variable inputs when looking for the optimal inclination, which you'll do next.

Closing out your trade study

Close out your trade study for the next section.

  1. Bring the Data Explorer window to the front.
  2. Close the Data Explorer window.
  3. Click No when prompted to close your trade study without saving.

    4. This will also close all open plots and graphs.

  4. Leave the Parametric Study tool open.

Refining the trade study parameters

Since you want to ensure that your orbit will cover the entire ice cap, you want to run a more refined parametric study in the area of interest.

  1. Return to the Parametric Study tool.
  2. Set the following Design Variable values:
    3. Option Value
    starting value 85
    ending value 95
    step size 1

    Using a large step size will speed up the analysis. A smaller step size will increase the number of samples. A smaller step size will give you more precise data but will take longer to run.

  3. Click Run.

Reviewing data in the Data Explorer Table

While you can create line plots that are great for presentations or personal choice, you can also obtain the required information directly from the Table page.

  1. Bring the Data Explorer window to the front when the when the trade study is finished running.
  2. Examine the results in the Data Explorer Table on the Table Page.

    3. Data Explorer Table

  3. Right-click on the maximum dependent variable (Model.STK_ODTK13.SensorOpt.Arctic_Monitor.CoveragePerDay.Overall_Value.Maximum) in the Data Explorer Table.
  4. Select Sort Runs in the shortcut menu.
  5. Select Descending in the Sort Runs submenu.

    6. The very first run in the Data Explorer Table (run 6) will be the run with the highest maximum coverage time.

    This study gives you a much better understanding of where to position the satellite to give you the best overall inclination to ensure maximum coverage of the whole ice cap. You can see that inclinations between 87 and 93 degrees will give you at least 2,000 seconds of maximum coverage of the ice cap during your analysis period. 90 Degrees has the highest amount of maximum coverage.

  6. Close the Data Explorer window.
  7. Click No when prompted to close your trade study without saving.
  8. Leave the Parametric Study tool open.

Updating the Inclination input variable for further study

As noted earlier, the closer the inclination is to 90 degrees, the better your maximum coverage will be. Set the inclination value to 90 for future studies so you can better understand the effects the other variables have on coverage.

  1. Click into the Inclination () Value field in the Component Tree.
  2. Enter 90.
  3. Select the Enter key to set LEO's inclination to 90 degrees.

Analyzing the impact of RAAN on coverage

The satellite's RAAN (right ascension of the ascending node) might impact your coverage.

Running a new Parametric Study

Build a new Parametric Study using the satellite's RAAN as your Design Variable.

  1. Click and drag the RAAN () input variable from the Component Tree to the Design Variable field when the Parametric Study tool opens.

    2. This will replace Inclination as the Design Variable.

  2. Set the following Design Variable values:
    3. Option Value
    starting value 0
    ending value 360
    step size 30
  3. Click Run.

Reviewing the trade study data

Review the table data and create a 2D Line Plot to gain understanding of how the satellite's RAAN affects coverage.

  1. Bring the Data Explorer window to the front when the when the trade study is finished running.
  2. Use your cursor to expand the table of runs so that you can see all thirteen runs.
  3. Look at the data in the Data Explorer Table.

    4. At first glance, the data appear to be fairly insensitive to RAAN. This may be due to the difference in scales minimum and maximum coverage values. To view just the minimum coverage values, create a new graph.

  4. Click Add View () on the Data Explorer toolbar.
  5. Select 2D Line Plot () in the drop-down menu.

    6. minimum seconds VS. RAAn

    Minimum coverage values fluctuate for different RAAN values. This is an artifact of the low frequency sampling of the data. While the difference between the high and low values is less than 10 percent of the mean, there are definitely some values that are better than others.

  6. Bring the Data Explorer window to the front.
  7. Sort the runs and determine which RAAN provides the highest maximum coverage (in this case, 0/360 degrees).

Closing out your trade study

Close out your trade study for the next section.

  1. Close the Data Explorer window when you are finished.
  2. Click No when prompted to close your trade study without saving.
  3. Leave the Parametric Study tool open.

Updating the RAAN input variable for further study

A RAAN of 0 degrees slightly improves your maximum coverage.

  1. Click into the RAAN () Value field in the Component Tree.
  2. Enter 0.
  3. Select the Enter key to set LEO's RAAN to 0 degrees.

Analyzing the impact of the semi-major axis on coverage

The final orbit parameter impacting coverage is the satellite's semi-major axis. Vary the semi-major axis from 6,500 through 7,500 kilometers.

Running a new Parametric Study

Build a new Parametric Study using the satellite's semi major axis as your Design Variable.

  1. Click and drag SemiMajorAxis () from the Component Tree to the Design Variable field when the Parametric Study tool opens.

    2. This will replace RAAN as the Design Variable.

  2. Set the following Design Variable values:
    3. Option Value
    starting value 6500
    ending value 7500
    step size 100
  3. Click Run.

Reviewing the trade study data

Review the table data and create a 2D Line Plot to gain understanding of how the satellite's RAAN affects coverage.

  1. Bring the Data Explorer window to the front when the when the trade study is finished running.
  2. Click Add View () on the Data Explorer toolbar.
  3. Select 2D Line Plot () in the drop-down menu.

Updating the 2D Line Plot's variables

Adjust the 2D Line Plot's variables and examine it for trends.

  1. Click Dimensions () in the Plot Options menu on the left-hand side of the 2D Line Plot.
  2. Click Add Series (+) to create Series 2.
  3. Set x to SemiMajorAxis.
  4. Set y to Maximum.
  5. Click Add Series (+) to create Series 3.
  6. Set x to SemiMajorAxis.
  7. Set y to Average.
  8. Click on the plot to close the Plot Options menu.

Reviewing the 2D Line Plot

With your series added, review the plot.

  1. Review the 2D Line Plot.

    2. Minimum, Maximum, and average seconds vs. Semi-major Axis

    There is an interesting trend here. The maximum and average coverage extents increase rapidly with the semi-major axis, but only until a certain point is reached; after that point, there is a drop off. The minimum extent of coverage continues to increase even as the maximum and average extents of coverage decrease. This is due to a required five-meter sensor resolution, since you need to be able to resolve icebergs as small as five meters in diameter. Because the sensor swath also increases, the minimum coverage subsequently decreases beyond a certain point, since the sensor can no longer resolve objects of five meters or smaller.

  2. Hover your cursor on the highest maximum design point in the plot to obtain information on the point.

    3. The conclusion reached from this trade study is that your maximum coverage extent is best with a semi-major axis of about 6,800 km.

  3. Close the Data Explorer window when you are finished.
  4. Click No when prompted to close your trade study without saving.
  5. Minimize the Parametric Study tool so that you can see the Analysis View.

Studying the sensor's Ground Sample Distance

Limitations to a sensor's resolution can be defined in terms of its Ground Sample Distance. The Ground Sample Distance is the smallest size of an object on the ground that can be detected by the sensor. It is based upon the access geometry and the physical attributes of the sensor. The sensor is modeled as capturing an array of pixels, where each pixel has the same sized square shape when projected in front of the sensor. The sensor is also assumed to be pointed directly at the target. When the sensor is looking straight down on the target, the size of the pixel on the ground is simply the size of the square projected to the distance of the ground. As a single pixel is the smallest element of the image, this distance, which is denoted as the GSD, represents the smallest discernible feature size in the image.

The Sensor object's five-meter resolution can might have an impact on your trade study. Confirm this by rerunning the Parametric Study with the sensor's Ground Sample Distance constraint effectively disabled.

Adding the constraint as an additional variable

Before you can study the impact of the Ground Sample Distance, you must add the constraint as a variable to your workflow.

  1. Right-click on the STK_ODTK13 component in the Analysis View.
  2. Select Show Component's GUI () in the shortcut menu.

    3. This will open the STK scenario and STK Analyzer windows. Please be patient.

  3. Bring the ModelCenter application window to the front if needed.
  4. Expand () LEO () in the STK Variables tree when the STK Analyzer window opens.
  5. Select Ice_Finder ().
  6. Select the Active Constraints tab in the STK Property Variables panel.
  7. Select and move () GroundSampleDistance.max to the Analyzer Variables list.

    8. Note that GroundSampleDistance.max is now listed as an input variable.

  8. Click OK to confirm your changes and to close the STK Analyzer window.

Updating the SemiMajorAxis, Inclination and RAAN input variables for further study

The closer the semi major axis is to 6800 kilometers, the better your maximum coverage will be. Set the semi major axis value to 6,800 kilometers for future studies. Also, reset the inclination variable to 90 degrees and the RAAN variable to 0.

  1. Click into the SemiMajorAxis () Value field in the Component Tree.
  2. Enter 6800.
  3. Select the Enter key.
  4. Click into the Inclination () Value field in the Component Tree.
  5. Enter 90.
  6. Select the Enter key.
  7. Click into the RAAN () Value field in the Component Tree.
  8. Enter 0.
  9. Select the Enter key.

When you opened Analyzer and then closed it, the Component Tree reverted the original settings that are in the scenario. You're resetting them to the values that provide the maximum coverage time, which you determined in the previous trade studies.

Updating the Ground Sample Distance

Rather than removing the constraint entirely, you can use an extremely large number to effectively remove the maximum GSD constraint.

  1. In the Component Tree, expand () Ice_Finder ().
  2. Expand () GroundSampleDistance ().
  3. Click into the max () Value field in the Component Tree.
  4. Enter 1e+300.
  5. Select the Enter key.

Rerunning the Parametric Study

With the GSD constraint effectively disabled, rerun the Parametric Study.

  1. Restore the Parametric Study tool, which you minimized previously.
  2. Click Run.
  3. Click Add View () on the Data Explorer toolbar when the trade study is complete.
  4. Select 2D Line Plot () in the drop-down menu.

    5. Minimum Seconds vs. Semi-major Axis without GSD Constraint

    Not altogether surprisingly, the plot indicates that without a Ground Sample Distance constraint, as the semi-major axis increases, the extent of coverage also increases.

  5. Close the Data Explorer window when you are finished.
  6. Click No when prompted to close your trade study without saving.
  7. Close the Parametric Study Tool.

Resetting the Sensor object's Ground Sample Distance

Reset the Sensor object's Ground Sample Distance constraint for further trade studies.

  1. Click into the max () Value field in the Component Tree.
  2. Enter 5.
  3. Select the Enter key.
  4. Save () your ModelCenter project.

Analyzing the effects of semi-major axis and inclination together

You have determined that inclination and the semi-major axis have significant impacts on coverage capability while the RAAN has minimal influence. The semi-major axis had an increasingly positive impact until the Ground Sample Distance constraint came into effect. Coverage generally improves as the inclination approaches 90 degrees. This leads to two questions: Does changing the semi-major axis impact your conclusions about inclination? And can you improve your sensor characteristics to permit a higher orbit? Answer the first question by performing a multidimensional Parametric Study (Carpet Plot).

Using the Carpet Plot tool

A Carpet Plot is a means of displaying data dependent on two variables in a format that makes interpretation easier than normal multiple curve plots. A Carpet Plot can be thought of as a multidimensional Parametric Study. Setting the design variables in a Carpet Plot is similar to using the Parametric Study tool, except you now have two variables instead of one.

  1. Click Carpet Plot () on the Standard toolbar.
  2. Click and drag Inclination () from the Component Tree to the first Design Variables field when the Carpet Plot tool opens.
  3. Set the following Inclination Design Variable values:
    4. Option Value
    From 85
    To 95
    Step Size 2
  4. Click and drag SemiMajorAxis () from the Component Tree to the second Design Variables field.
  5. Set the following SemiMajorAxis Design Variable values:
    6. Option Value
    From 6500
    To 7500
    Step Size 200
  6. Click and drag Maximum () from the Component Tree to the Responses field.
  7. Click Run.

Determining the best inclination and semi major axis

Sort the data in the Data Explorer window to determine the best inclination and semi major axis values that provide maximum coverage.

  1. Close the Carpet Plot when the trade study is finished running.
  2. Bring the Data Explorer window to the front.
  3. Sort the runs to determine which combination of inclination and semi major axis provides the highest maximum coverage.

An inclination of 89 degrees and a semi major axis of 6,900 kilometers is the best choice.

Creating a Scatter Matrix

Create a Scatter Matrix from the Data Explorer to better visualize your trade study. A Scatter Matrix displays a grid of graphs that compare every design variable and response against every other design variable and response in the trade study. Using these graphs, it's possible to quickly gain understanding as to the relationship between various variables in your trade study.

  1. Click Add View () on the Data Explorer toolbar.
  2. Select Scatter Matrix () in the drop-down menu.
  3. Review the Scatter Matrix.
  4. Focus on the Maximum - SemiMajorAxes plot.
  5. Maximize the Scatter Matrix.
  6. Hover your cursor over the highest point.
  7. Move the cursor up and down.

    8. Depending on your screen size and resolution, multiple points could be sitting very close to each other on the plot. You should get two different Design Tooltips: one showing and inclination of 89 degrees and another showing an inclination of 91 degrees.

  8. Click on the point showing 89 degrees.

    9. This will highlight the data points in all three plots that correspond to the point that you selected.

  9. Hover your cursor over the selected plot.

    10. This will provide information on the selected point. As with the 2D Line Plot, you can also open the Design View dialog box to see the data in tabular form.

scatter matrix

You can also click Zoom () on the Scatter Matrix toolbar and draw multiple boxes around the points until they are visually separated. A 3D Scatter Plot is another easy way to visualize the output of your trade study.

Closing out your trade study

Close out your trade study for the next section.

  1. Close the Data Explorer window when you are finished.
  2. Click No when prompted to close your trade study without saving.
  3. Close the Carpet Plot tool.

You will update the SemiMajorAxis and Inclination later with these new values.

Adding additional variables to study the sensor's resolution

You now know that for any given inclination, increasing the orbit's semi-major axis will improve coverage. However, you must take into account the five-meter Ground Sample Distance constraint for the Sensor object. You can study Ice_Finder's resolution properties to permit greater viewing capabilities at higher orbits, but you must first add the component variables, focal length and detector pitch, to your model.

  1. Right-click on the STK_ODTK13 component in the Analysis View.
  2. Select Show Component's GUI () in the shortcut menu.
  3. Expand () LEO () in the STK Variables tree when the STK Analyzer window opens.
  4. Select Ice_Finder ().
  5. Move () the SimpleConic () property in the STK Property Variables tree to the Analyzer Variables list.

    6. This will add coneAngle as an input variable.

  6. Move () the Resolution () property to the Analyzer Variables list.

    7. This will add both FocalLength and DetectorPitch as input variables.

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

Updating the SemiMajorAxis, Inclination and RAAN input variables for further study

Set the semi major axis, inclination and RAAN values to your best values from your previous trade studies.

  1. Click into the SemiMajorAxis () Value field in the Component Tree.
  2. Enter 6900.
  3. Select the Enter key.
  4. Click into the Inclination () Value field in the Component Tree.
  5. Enter 89.
  6. Select the Enter key.
  7. Click into the RAAN () Value field in the Component Tree.
  8. Enter 0.
  9. Select the Enter key.

Studying the sensor's detector pitch

Determine the impact of varying the sensor's detector pitch on coverage.

Running a Parametric Study

Build a new Parametric Study using DetectorPitch as your Design Variable. You will focus on maximum coverage for now.

  1. Expand () the SimpleConic () and Resolution () components in the Component Tree.
  2. Click Parametric Study () on the Standard toolbar.
  3. Click and drag DetectorPitch () from the Component Tree to the Design Variable field.
  4. Set the following DetectorPitch Design Variable values:
    5. Option Value
    starting value 0.0001
    ending value 0.001
    step size 0.0001
  5. Click and drag Maximum () from the Component Tree to the Responses field.
  6. Click Run.

Creating a 2D Line Plot

Create a 2D Line Plot to investigate the data.

  1. Bring the Data Explorer window to the front when the when the trade study is finished running.
  2. Click Add View () on the Data Explorer toolbar.
  3. Select 2D Line Plot () in the drop-down menu.
  4. Click Axes () in the Plot Options menu.
  5. Select the Ticks tab.
  6. Change the Max # value to 30.
  7. Click anywhere on the plot to close the Plot Options menu.
  8. Review the 2D Line Plot.

Maximum Seconds vs. Detector Pitch

The detector pitch has a maximum threshold value of approximately 0.0003 meter, which, if exceeded, will result in degraded coverage capabilities.

Closing out your trade study

Close out your trade study for the next section.

  1. Close the Data Explorer window when you are finished.
  2. Click No when prompted to close your trade study without saving.
  3. Leave the Parametric Study tool open.
  4. Click into the DetectorPitch () Value field in the Component Tree.
  5. Enter 0.0001.
  6. Select the Enter key.

Studying the sensor's focal length

Determine the impact of focal length on coverage.

Running a Parametric Study

Build a new Parametric Study using FocalLength as your Design Variable.

  1. Return to the Parametric Study tool.
  2. Click and drag FocalLength () from the Component Tree to the Design Variable field.

    3. This will replace DetectorPitch as the Design Variable.

  3. Set the following FocalLength Design Variable values:
    4. Option Value
    starting value 50
    ending value 200
    step size 10
  4. Click Run.

Creating a 2D Line Plot

Create a 2D Line Plot to investigate the data.

  1. Bring the Data Explorer window to the front when the when the trade study is finished running.
  2. Click Add View () on the Data Explorer toolbar.
  3. Select 2D Line Plot () in the drop-down menu.
  4. Review the 2D Line Plot.

Maximum Seconds vs. Focal Length

There isn't comparatively that much of a difference, but a focal length of 110 meters gives you the best maximum coverage.

Closing out your trade study

Close out your trade study for the next section.

  1. Close the Data Explorer window when you are finished.
  2. Click No when prompted to close your trade study without saving.
  3. Leave the Parametric Study tool open.
  4. Click into the FocalLength () Value field in the Component Tree.
  5. Enter 110.
  6. Select the Enter key.

Studying the sensor's cone angle

Determine the impact of the cone angle sensor parameter.

Running a Parametric Study

Build a new Parametric Study using coneAngle as your Design Variable.

  1. Return to the Parametric Study tool.
  2. Click and drag coneAngle () from the Component Tree to the Design Variable field.
  3. Set the following coneAngle Design Variable values:
    4. Option Value
    starting value 30
    ending value 80
    step size 5
  4. Click Run.

Creating a 2D Line plot

Create a 2D line plot to investigate the data.

  1. Bring the Data Explorer window to the front when the when the trade study is finished running.
  2. Click Add View () on the Data Explorer toolbar.
  3. Select 2D Line Plot () in the drop-down menu.
  4. Review the plot.

Maximum Seconds vs. Cone Angle

The cone angle has a threshold value of approximately 70 degrees.

Closing out your trade study

Close out your trade study for the next section.

  1. Close the Data Explorer window when you are finished.
  2. Click No when prompted to close your trade study without saving.
  3. Close the Parametric Study tool.
  4. Click into the coneAngle () Value field in the Component Tree.
  5. Enter 70.
  6. Select the Enter key.

Analyzing your final input variable values

You can quickly analyze your final settings by running the current workflow.

  1. Click Run () on the Standard toolbar.
  2. When completed, note the output variable values.

    3. You can see that you have a vast improvement in all your output variable values compared to the starting values at the beginning of the scenario.

  3. Save () your ModelCenter project.

Optimizing the sensor with the Optimization tool

Sensor parameters have a large impact on coverage. You may have minimum or maximum thresholds you must meet as part of your mission — for example, a minimum coverage time, or a maximum focal length. Although you can see some trends from the previous studies, guessing at the sensor's optimum values will be difficult because you are dealing with multiple input variables at the same time, and your trade studies thus far only changed one or two parameters at a time.

Instead of continuing to guess at these parameters, you can use the STK Analyzer Optimization capability, by means of the ModelCenter software's Optimization tool, to study and optimize them all at once. 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. Use the tool to both minimize the focal length requirement for the sensor and to optimize the other sensor parameters, all while maintaining a notional, minimum coverage of 300 seconds per day for your coverage area.

Creating an objective

Objective functions can be specific variables or equations composed of multiple output variables.

  1. Click Optimization Tool () on the Standard toolbar.
  2. Click and Drag FocalLength () from the Component Tree to the Objective field on the right when the Optimization tool opens.
  3. Ensure the Goal is set to minimize.

Adding a constraint

Constraints restrict particular variables to a region or value.

  1. Click and drag Minimum () to the Constraint field.
  2. Click into the Lower Bound field
  3. Enter 300.
  4. Select the Enter key.
  5. Leave the Upper Bound blank.

    6. Since there is no upper bound, you can leave it undefined.

Selecting the Design Variables

The design variables are the variables that the Optimization tool will modify to meet the objective. You want the optimizer to minimize the FocalLength by changing coneAngle, FocalLength, and DetectorPitch.

  1. Click and drag coneAngle (), FocalLength (), and DetectorPitch () from the Component Tree to first Design Variables field.
  2. Enter the following Design Variable values:
    3. Design Variable Start Value (Explicit Value) Lower Bound Upper Bound
    coneAngle 70 60 80
    FocalLength 110 90 130
    DetectorPitch 0.0001 0.0001 0.001

Note that each Start Value must be equal to or greater than its respective Lower Bound value. In this case, you are starting with your baseline detector parameters.

optimization tool values

Selecting the algorithm

Many algorithms are available, including gradient-based optimizers, genetic algorithms, multiobjective algorithms, and other heuristic search methods.

  1. Open the Algorithm drop-down list.
  2. Select optiSLang Optimizer OCO Algorithm.

    3. The Ansys ModelCenter software is integrated with five algorithms from the Ansys optiSLang® process integration and design optimization software. Ansys optiSLang is used by a wide range of industries for parametric design exploration, optimization, and robustness analysis in combination with any simulation or computer-aided engineering (CAE) tools. The integration of optiSLang optimizers allows you to perform efficient parameter optimization, design exploration optimal trade-off identification, and cost-effective solutions.

    The optiSLang One Click Optimizer (OCO) abstracts the complexity of optimization algorithms away from the end-user. Internally, numerous optimization algorithms and metamodels are used to find the best objective(s). OCO is an efficient hybrid optimization strategy that comes with only one major setting to be tuned: the maximum number of design evaluations. Depending on the type and number of input parameters and the defined optimization criteria, the optimizer automatically selects the most suitable optimization algorithms with their most appropriate settings to solve the optimization problem. The ability to dynamically switch between optimization algorithms and to run multiple algorithms simultaneously makes OCO one of the most reliable and efficient optimization strategies. OCO is a surrogate-assisted optimization strategy, using capabilities of the Metamodel of Optimal Prognosis (MOP) for function approximation to significantly speed up the optimization process.

  3. Click Options....
  4. Note the Maximum number of design evaluations is set to 500 when the Options dialog opens.

    5. This is the maximum number of design evaluations the algorithm will compute before stopping.

  5. Click Cancel to close the Options Dialog without making any changes.

Running the optimization study

You are interested in the best design values.

  1. Click Run.

    2. Be patient. Your optimization study will take a while to complete.

  2. View the 2D Scatter Plot that the Optimization tool automatically created for you.

    3. Optimization tool 2D Scatter Plot, zOOMED IN TO FIRST 250 RUNS

    Your plot will look different than the one above. Note how the algorithm narrowed the range of feasible results, then converged around a minimum focal length solution as the number of runs progressed.

    You can see a plot of the convergence history on the Convergence History tab in the Optimization Tool Results window.

  3. Close the 2D Scatter Plot when you are finished.
  4. Return to the Optimization tool.
  5. Click View Output... in the Status panel to show the convergence history of the process.
  6. Select the Best Design tab, which contains the optimized values, when the Optimization Tool Results window opens.

    7. optimization tool Best design values

    These values are also displayed in the Value column for the design variables in the Optimization tool.

    Your results for the design variable values and the best design run number will be different from the above image. In this case, while the algorithm continued on and converged around a solution, the overall best value was from an earlier run.

  7. Close the Optimization Tool Results window when you are finished.

After running an optimization study, the values in your model will be changed to the final, optimized values. In this case, your optimal minimum values were at the limits of your design specifications.

Saving your work

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.

Summary

You wanted to understand how a LEO satellite's orbital and sensor parameters impact coverage capabilities. Your solution for this problem was to optimally configure the satellite's orbit and sensor to best cover the polar ice cap. You did this by running a series of parametric studies. For each parametric study, you analyzed a single design parameter through a sweep of values. Next you created a carpet plot to view how multiple parameters impact coverage. Finally, you used the Optimization tool to scan through the sensor parameter design space to find a solution that met your requirements.

On your own

You can run another optimization study, which takes into account not only the sensor parameters, but also the satellite's orbital parameters, which you iterated towards manually. The more input variables you study, however, the longer your study may take and the more runs you may require to find an optimized value. When you find your best design, you can click Copy to copy the text and data on the Best Design tab and paste it into a text file for reference. You can then use this reference file to enter the values into the STK application for further study.