Performing Trade Studies Using Analyzer
STK Premium (Air), STK Premium (Space), or STK Enterprise
You can obtain the necessary licenses for this training by visiting http://licensing.agi.com/stk/evaluation or contacting AGI Support at support@agi.com or 1-800-924-7244.
Additional installation - Analyzer.
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:
- STK Core
- Coverage
- STK Analyzer
Problem
Engineers and operators require a quick way to determine how various orbital parameters will effect the ability of a sensor or camera to view the surface of the Earth. Your team wants to launch a satellite into orbit that will be used to monitor icebergs over the polar cap. You will use a low Earth orbit (LEO) satellite to scan the Earth's surface. Data will then be relayed through a GEO satellite back to a ground processing facility in Montreal. Your purpose is to better understand the requirements for the LEO satellite to include specifying orbit parameters for the satellite and configuration of the sensor.
Solution
To better understand how the LEO satellite orbit and sensor parameters impact coverage capabilities, a series of parametric studies will be run. For each parametric study, a single design parameter will be run through a sweep of values. At each value, coverage statistics will be collected using a Figure of Merit.Your solution for this problem is to optimally configure the satellite’s orbit and sensor to best cover the polar ice cap. To initiate your analysis, you will perform a few trade studies to see how changing parameters impacts your coverage capability. This will be followed by creation of a carpet plot to view how multiple parameters impact coverage. Lastly, an optimization study will be performed to scan through the design space to find a solution that meets your requirements.
What you will learn
Upon completion of this tutorial, you will understand how to:
- Parametrically explore the STK 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.
Analyzer
Watch the following video, then follow the steps below incorporating the systems and missions you work on (sample inputs provided).Implementing the starter scenario (*.vdf file)
To speed things up and enable you to focus on this lesson's main goal, you will use a partially created scenario. The partially created scenario is saved as a visual data file (VDF) in the STK Data Federate.
- Launch STK ().
- Click Open a Scenario () in the Welcome to STK dialog.
- If you are using STK 12.6 or older, skip to step 6.
- If you are using STK 12.7 or newer, open the Location: shortcut menu in the Open dialog.
- Select STK Data Federate.
- If you are using STK 12.6 or older, click STK Data Federate on the left side of the Open dialog box.
- Select the Browse tab when connected to the STK Data Federate.
- Browser to <AGI SEDS SDF - Sites - AGI - documentLibrary - STK 12 - Starter Tutorials>.
- Select SensorOpt.vdf (v1.0).
- Click .
Visual data files versus Scenario files
When you open a VDF file, STK keeps it as a VDF and does not automatically convert it to a scenario file. This means, STK does not change the file type of your scenario when you launch your scenario. You must make sure that you save your work in STK as a scenario file (.sc) and not a visual data file (.vdf). A VDF is a compressed version of an STK scenario, which makes them great for sending your work in STK to others. However, you want to use a scenario file while working with STK on your machine. You need to convert the VDF to a Scenario file using Save As.
Saving a VDF file as a Scenario file
You will select Save as from the STK File menu to convert the VDF file that you opened into a scenario file.
- Open the File menu.
- Select Save As...
- If you are using STK 12.6 or older, skip to step 6.
- If you are using STK 12.7 or newer, open the Location: shortcut menu.
- Select File System.
- Select STK User on the left side of the Save As dialog box.
- Select SensorOpt.
- Click .
- Open the Save as type: shortcut menu.
- Select Scenario Files (*.sc).
- Select the file SensorOpt.
- Click .
- Click to confirm.
Animate the scenario for situational awareness
Slow your animation down and animate the scenario. You can view the link from Montreal () to GEO_Relay() to LEO () to LEO/Ice_Finder ().
- Click Decrease Time Step () until Time Step: is set at 10:00 sec.
- Click Start () to animate the scenario.
- View the LEO () scan the polar ice cap.
- Click Reset () when finished.
Compute Accesses Tool
The ultimate goal of coverage is to analyze accesses to an area using assigned assets and applying necessary limitations upon those accesses. Compute coverage with the Compute Accesses tool. Arctic_Monitor's () grid area of interest is the Area Target () named Arctic. Arctic_Monitor's () asset is Relay_Chain ().
- Right-click Arctic_Monitor () in the Object Browser.
- Select CoverageDefinition in the shortcut menu.
- Select Compute Accesses in the second shortcut menu.
Grid Stats Report
Your scenario analysis time is seven (7) days. CoveragePerDay's () definition is set to Coverage Time and computing Per Day. Per Day is the total coverage time divided by the number of days in the coverage interval. You will use Analyzer to perform trade studies on CoveragePerDay's () Grid Stats report. To understand this report, data will first be manually collected in STK. Generate a Grid Stats report to see the smallest to largest number of accesses to any point in the grid.
- Right-click on CoveragePerDay () in the Object Browser.
- Select Report & Graph Manager... () in the shortcut menu.
- Select Grid Stats report () in the Installed Styles list when the Report & Graph Manager opens.
- Click .
- In the resulting report, note the Minimum, Maximum, and Average values. These values will be accessible in Analyzer as output variables.
- When Finished, close the Grid Stats report and the Report & Graph Manager.
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 (Minimum=0), at least one point is seen for ~662 seconds and on average points are seen for ~219 seconds during your analysis period.
Analyzer
Analyzer provides a set of analysis tools that:
- Enable you to understand the design space of your systems.
- Enable you to perform analyses in STK easily, without involving programming or scripting.
- Introduce trade study and post-processing capabilities.
- Can be used with all STK scenarios, including those with STK Astrogator satellites.
- Click View on the STK menu bar.
- Select Toolbars.
- Select Analyzer.
- Click Analyzer... () on the Analyzer toolbar.
Start by opening Analyzer.
Analyzer imports a copy of the currently loaded Scenario. Any of the STK variables can be added as Analyzer input or output variables. If you change a value of a variable in your Scenario through the STK interface, you should re-add the variable as an Analyzer variable before running any trade studies with the new value.
Select satellite input variables
You will start by selecting the following satellite orbit variables:
- Inclination
- RAAN
- Semi-major Axis
- Select LEO () in the STK Variables list.
- Expand () Propagator (J4Perturbation) () in the STK Property Variables list.
- Double click on the following STK Property Variables to move them to the Analyzer Variables list.
- SemiMajorAxis ()
- Inclination ()
- RAAN ()
Select Figure of Merit output variables
The output variables will be average, minimum and maximum coverage per day of the Arctic Monitor.
- Expand () Arctic_Monitor () in the STK Variables list.
- Select CoververagePerDay ().
- Expand () Overall Value () in the Data Provider Variables list.
- Double click on the following data providers to move them to the Analyzer Variables list:
- Minimum ()
- Maximum ()
- Average ()
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.
- Click Parametric Study... () on the Analyzer toolbar to open the Parametric Study Tool.
Parametric Study tool
The tool contains the Component Tree on the left that lists variables that you selected in Analyzer. The fields on the right are used to specify what variables should be used in the study.
Inclination Parametric Study
Set up a Parametric Study with Inclination as the design variable.
- Drag and drop the Design Variable, Inclination (), from the Component Tree on the left to the Parametric Study Tool's Design Variable on the right.
- Set the following Design Variable parameters:
- Drag and drop the following data providers into the Responses field:
- Minimum ()
- Maximum ()
- Average ()
- Click
Option | Value |
---|---|
starting value: | 45 |
ending value: | 135 |
step size: | 10 |
Completed Parametric Study
Data Explorer
The Data Explorer is a Trade Study tool used to display data collected from STK. While data is being collected in the Table, the Data Explorer window displays a progress meter, a halt button, and the data. Once the Parametric study is complete, the Table page and 2D Scatter Plot display the collected data.
- Bring the Table Page to the front when all runs are completed.
- Click Add View in the Table Page toolbar.
- Select 2D Line Plot in the shortcut menu.
Table Page
Customize
Update the graph to display each Inclination vs the Maximum, Minimum, and Average coverage time.
- Click in the menu on the left.
- Open the y shortcut menu in the Dimensions dialog box.
- Select Maximum. This changes Series 1 to Maximum (sec).
- Click at the top of the Dimensions dialog box. This creates Series 2.
- Open the x shortcut menu.
- Select Inclination.
- Open the y shortcut menu.
- Select Minimum. This changes Series 2 to Minimum(sec).
- Click at the top of the Dimensions dialog box. This creates Series 3.
- Open the x shortcut menu.
- Select Inclination.
- Open the y shortcut menu.
- Select Average. This changes Series 3 to Average (sec).
- Click on the graph to exit out of the menu.
- Bring the Table Page to the front.
- Close the Table Page.
- Click when asked to save the study. This will close any graphs associated with the trade study.
2D Line Plot
Results from the first study are not unexpected: the closer the inclination is to 90 degrees, the better your coverage capability 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 are two additional interesting trends in the data. First, maximum coverage does not smoothly improve as inclination approaches 90 degrees. Second, and more importantly, the minimum coverage value does not climb above zero until inclination reaches some value between 75 and 90 degrees.
Since you want to ensure that your orbit will cover the entire ice cap, run a more refined parametric study in the area of interest.
Refine the trade study parameters
- Return to the Parametric Study Tool. If you don't see it, it might be located behind Analyzer.
- Set the following Design Variable parameters:
- Click .
Option | Value |
---|---|
starting value: | 85 |
ending value: | 95 |
step size: | 1 |
Table Page Data
You can create line plots which are great for presentations or personal choice, but you can also obtain the required information from the Table Page.
- Bring the Table Page to the front when all runs are completed.
- Use your cursor to expand the table of runs so that you can see all eleven (11) runs.
- Close the Table Page.
- Click when asked to save the study.
- Return to the Parametric Study Tool.
This study gives us a much better understanding of where to position the satellite to give us the best overall inclination to assure maximum coverage of the whole ice cap. You can see that inclinations between 87 and 93 degrees will ensure us of at least 2000 plus seconds of maximum coverage of the ice cap during your analysis period.
Sync data from the Parametric Study Tool to STK
You can sync data from STK into the Parametric Study Tool or vice versa. You can make changes in the Component Tree and sync the changes back to STK.
- Click on the Inclination value in the Component Tree.
- Enter the value 90.
- Click the Enter key on your keyboard.
- Click at the bottom of the Component Tree. This sets LEO's () inclination to 90 degrees in STK. It also recomputes coverage.
- Return to the Parametric Study Tool.
Determine the impact of RAAN on coverage
RAAN (right ascension of the ascending node) might impact your coverage.
- Highlight everything in the Design Variable field.
- Click the Back key on your keyboard. This clears the variable so that you can enter a new variable.
- Drag and drop the Design Variable, RAAN (), from the Component Tree on the left to the Parametric Study Tool on the right.
- Set the following Design Variable parameters:
- Click .
Option | Value |
---|---|
starting value: | 0 |
ending value: | 360 |
step size: | 30 |
Table Page
- Bring the Table Page to the front when all runs are completed.
- Use your cursor to expand the table of runs so that you can see all thirteen (13) runs.
- Look at the data in the Table Page.
- Click Add View in the Table Page toolbar.
- Select 2D Line Plot in the shortcut menu.
- Bring the Table Page to the front.
- Close the Table Page.
- Click when asked to save the study.
- Return to the Parametric Study Tool.
At first glance the data appears 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.
minimum time versus 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 high and low values is less than 10 percent of the mean, there are definitely some values that are better than others.
Determine the Impacts of Altitude on Coverage
The final orbit parameter impacting coverage is the altitude of the orbit, or expressed in classical orbit parameters; the semi-major axis. Vary the orbit from 6,500 to 7,500 kilometers.
- Clear RAAN from the Design Variable field.
- Drag and drop the Design Variable, SemiMajorAxis (), from the Component Tree on the left to the Parametric Study Tool on the right.
- Set the following Design Variable parameters:
- Click .
Option | Value |
---|---|
starting value: | 6500 |
ending value: | 7500 |
step size: | 100 |
Table Page
Obtain the required information from the Table Page.
- Bring the Table Page to the front.
- Use your cursor to expand the table of runs so that you can see all eleven (11) runs.
- Close the Table Page.
- Click when asked to save the study.
There is an interesting trend here. Maximum and average coverage increases rapidly with altitude until a certain altitude is reached at which point there is an equally sharp drop off. Minimum coverage continues to increase even as maximum and average coverage decreases. This is due to a resolution constraint of 5 meters – you need to be able to resolve icebergs as small as 5 meters in diameter. Coverage capabilities increase with orbit altitude because the sensor swath also increases. They also decrease beyond a certain altitude because the sensor can no longer resolve 5 meter objects. Your conclusion from this trade study is that your maximum coverage capability is best with a semi-major axis of about 6,800 km.
Sensor Resolution
The Sensor () object's resolution constraint might have an impact on your trade study. Confirm this by rerunning the study with the Ground Sampling Distance constraint disabled.
- Bring STK to the front. You might need to move Analyzer and the Parametric Study Tool to the side in order to perform the following tasks.
- Right click on Ice_Finder () in the Object Browser.
- Select Properties () in the shortcut menu.
- Select the Constraints - Resolution page.
- Clear the Max: checkbox in the Ground Sample Distance frame.
- Click to accept your change and keep the Properties Browser open.
Rerun the Parametric Study
- Bring the Parametric Study Tool to the front.
- Click .
Table Page
Obtain the required information from the Table Page.
- Bring the Table Page to the front.
- Use your cursor to expand the table of runs so that you can see all eleven (11) runs.
- Close the Table Page.
- Click when asked to save the study.
- Close the Parametric Study Tool.
The resulting parametric study indicates that without a resolution constraint, as altitude increases, coverage capabilities also increase for all three (3) output variables.
Reset the Sensor object's resolution constraint
Reset the Sensor () object's resolution constraint for further trade studies
- Bring STK to the front.
- Return to Ice_Finder's () properties ().
- Select the Constraints - Resolution page.
- Select the Max: check box in the Ground Sample Distance frame.
- Click to accept your changes and to close the Properties Browser.
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 multi-dimensional Parametric Study.
You have determined that inclination and altitude have significant impacts on coverage capability while the RAAN has minimal influence. Altitude had an increasingly positive impact until the ground sample distance constraint came into effect. Inclination generally improves as we approach 90 degrees. This leads to two questions:
- Does changing altitude impact our conclusions about inclination?
- Can we improve our sensor characteristics to permit a higher altitude orbit?
- Return to Analyzer.
- Click Carpet Plot... () in the STK Analyzer toolbar to open the Carpet Plot Tool.
You will answer the first question by performing a multi-dimensional Parametric Study (Carpet Plot). You can answer the second question later in the scenario.
Study two variables
- Drag and drop the Design Variable, Inclination (), from the Component Tree on the left to the first Design Variables field on the right.
- Set the following Design Variables parameters:
- Drag and drop the Design Variable, SemiMajorAxis (), from the Component Tree on the left to the second Design Variables field on the right.
- Set the following Design Variables parameters:
- Drag and drop the following data provider elements into the Responses field.
Minimum ()
Maximum ()
Average ()
- Click . Be patient. This could take a couple of minutes.
Option | Value |
---|---|
From | 85 |
To | 105 |
Step Size | 5 |
Option | Value |
---|---|
From | 6500 |
To | 7500 |
Step Size | 200 |
Create a Contour Plot
- Bring the Table Page to the front when all runs are completed.
- Click Add View.
- Select Contour Plot in the shortcut menu.
Customize
Display Average versus SemiMajorAxis versus Inclination.
- Click Dimensions in the menu on the left.
- Open the z shortcut menu.
- Select Average.
- Click on the graph to exit out of the menu.
- Click on the graph to exit out of the menu.
Contour plot
The contour plot indicates that, regardless of altitude, the likely optimal inclination for the best average coverage time is around 90 degrees and the altitude is somewhere between 6800 and 7000 kilometers.
Create a 3D Scatter Plot
- Click Add View on the Contour Plot toolbar.
- Select 3D Scatter Plot in the shortcut menu.
Display Inclination vs Semi Major Axis vs Average coverage time
- Click Dimensions.
- Open the z shortcut menu.
- Select Average.
- Click on the graph to exit out of the menu.
- Bring the Table Page to the front.
- Close the Table Page.
- Click when asked to save the study.
- Close the Carpet Plot Tool.
3D Scatter Plot
Knowing the inclination is best at ~90 degrees and RAAN is relatively insignificant, your new goal is to improve your sensor characteristics to allow for greater orbit altitude and thus improve coverage.
Sensor Resolution
You now know that for any given inclination, increasing orbit altitude will improve coverage. However, you must take into account the ground sampling resolution constraint for the Sensor () object. Using the Resolution page, you can change Sensor () object properties to permit greater viewing capabilities at higher altitudes.
Sensor Input Variables
Select your Sensor () object input variables.
- Bring Analyzer to the front.
- Expand () LEO () in the STK Variables list.
- Select Ice_Finder ().
- Expand () SimpleConic () in the STK Property Variables list.
- Double click coneAngle () to move it to the Analyzer Variables list.
- Expand () Resolution () in the STK Property Variables list.
- Double click FocalLength () to move it to the Analyzer Variables list.
- Double click DetectorPitch () to move it to the Analyzer Variables list.
- Click Parametric Study... () on the Analyzer toolbar to open the Parametric Study Tool.
Sync data from the Parametric Study Tool to STK
Set the inclination back to 90 degrees.
- Click on the Inclination value in the Component Tree.
- Enter the value 90.
- Click the Enter key on your keyboard.
- Click at the bottom of the Component Tree. This sets LEO's () inclination to 90 degrees in STK.
- Return to the Parametric Study Tool.
Parametric Study / Detector Pitch
You will focus on maximum coverage for now.
- Drag and drop the Design Variable, DetectorPitch (), from the Component Tree on the left to the Parametric Study Tool on the right.
- Set the following Design Variable parameters:
- Drag and drop the Maximum () data provider into the Responses field.
- Click .
Option | Value |
---|---|
starting value: | .0001 |
ending value: | .001 |
step size: | .0001 |
2D Line Plot
- Bring the Table Page to the front when all runs are completed.
- Click Add View on the Table Page toolbar.
- Select 2D Line Plot in the shortcut menu.
- Click Axes in the menu on the left.
- Select Ticks in the Axes dialog box.
- Enter the value 20 in the Max # field.
- Click the Tab key on your keyboard.
- Click on the graph to close the Axex dialog.
- Bring the Table Page to the front.
- Close the Table Page.
- Click when asked to save the study.
Maximum Seconds vs. Detector Pitch
Detector pitch has a maximum threshold value (.0003 m), which if exceeded will result in degraded coverage capabilities.
Parametric Study / Focal Length
Determine the impacts of focal length on coverage.
- Return to the Parametric Study Tool.
- Clear DetectorPitch from the Design Variable field.
- Drag and drop the Design Variable, FocalLength (), from the Component Tree on the left to the Parametric Study Tool on the right.
- Set the following Design Variable parameters:
- Click .
Option | Value |
---|---|
starting value: | 50 |
ending value: | 200 |
step size: | 10 |
2D Line Plot
- Bring the Table Page to the front when all runs are completed.
- Click Add View on the Table Page toolbar.
- Select 2D Line Plot in the shortcut menu.
- Click Axes.
- Select Ticks in the Axes dialog box.
- Enter the value 20 in the Max # field.
- Click the Tab key on your keyboard.
- Click on the graph to close the Axes dialog.
- Bring the Table Page to the front.
- Close the Table Page.
- Click when asked to save the study
Maximum Seconds vs. Focal Length
Focal length has a threshold value of approximately 140 m that when reached, further increases don't improve coverage.
Parametric Study / Cone Angle
Determine the impact of the cone angle sensor parameter.
- Return to the Parametric Study Tool.
- Clear FocalLength from the Design Variable.
- Drag and drop the Design Variable, coneAngle (), from the Component Tree on the left to the Parametric Study Tool on the right.
- Set the following Design Variable parameters:
- Click .
Option | Value |
---|---|
starting value: | 20 |
ending value: | 60 |
step size: | 5 |
2D Line Plot
- Bring the Table Page to the front when all runs are completed.
- Click Add View on the Table Page toolbar.
- Select 2D Line Plot in the shortcut menu.
- Bring the Table Page to the front.
- Close the Table Page.
- Click when asked to save the study.
- Close the Parametric Study Tool.
Maximum Seconds vs. Cone Angle
The cone angle has a threshold value of approximately 50 degrees.
Optimization Tool
Sensor parameters have a large impact on coverage capabilities. In order to optimize these parameters, you can either guess at values or employ an optimization tool. Although you can see trends from the previous studies, guessing at values will be difficult because you are dealing with multiple parameters at the same time and the trends, thus far, assume only one or two parameters are changed at a time.
To solve more complex problems, an optimization tool can be a very useful. An optimizer is an automated tool that makes mathematical calculations about a design problem and incrementally attempts to find an optimal solution. You will use the optimizer to minimize the focal length requirement for the sensor while maintaining a minimum coverage capability of 150 seconds per day for your coverage area.
- Bring Analyzer to the front.
- Click Optimization Tool... () on the Analyzer toolbar to open the Optimization Tool.
- Click on the inclination value in the Component Tree.
- Enter the value 90.
- Click the Enter key on your keyboard.
- Click .
Objective
The objective functions can be specific variables or equations composed of multiple output variables.
- Return to the Optimization Tool.
- Drag and drop FocalLength () from the Component Tree on the left to the Objective list on the right in the Objective Definition frame.
- Check that the Value is 100 and the Goal is minimize. If you had two variables, one of them might have a value of 80 and the other 20. In this case there's only one value so it gets 100.
Constraints
Constraints restrict particular variables to a region or value.
- Drag and drop Minimum from the Component Tree on the left to the Constraint list on the right.
- Click twice in the cell below Lower Bound.
- Enter the value 150.
- Click the Tab key on your keyboard. There is no upper bound.
Design Variables
The design variables are the variables that the optimizer will modify to meet the objective. You want the optimizer to minimize the FocalLength by changing coneAngle, DetectorPitch, and FocalLength.
- Drag and drop coneAngle () from the Component Tree on the left to the Design Variables list on the right.
- Set the following Design Variable parameters:
- Drag and drop FocalLenth () from the Component Tree on the left to the Design Variable list on the right in the Design Variables frame.
- Set the following Design Variable parameters:
- Drag and drop DetectorPitch () from the Component Tree on the left to the Design Variables list on the right.
- Set the following Design Variable parameters:
Option | Value |
---|---|
Lower Bound | 20 |
Upper Bound | 60 |
Option | Value |
---|---|
Lower Bound | 50 |
Upper Bound | 200 |
Option | Value |
---|---|
Lower Bound | .0001 |
Upper Bound | .001 |
optimization tool values
Design Explorer
You will use the Design Explorer. Design Explorer is an advanced optimization algorithm that was developed to efficiently solve difficult real-world design problems.
- Open the shortcut menu in the Algorithm frame.
- Select Design Explorer.
- Click . Be patient. This will take a while to complete.
Optimization Tool Output
You are interested in the best design values.
- Return to the Optimization Tool when all runs are completed.
- Click .
- Select the Best Design tab when the Optimization Tool Results dialog box opens.
- When finished, click to close the Optimization Tool Results dialog box.
- Bring the Table Page to the front.
- Close the Table Page.
- Click when asked to save the study.
- Close the Optimization Tool.
- Click to save as a favorite.
- Close STK Analyzer.
optimization tool Best design values
After running an optimization study, the values in your Scenario will be changed to the final, optimized values. They will not be changed back to what they were before starting the study.
Save Your Work
Always remember to save your scenario!
- Return to STK.
- Save () your work.
Summary
You wanted to understand how a LEO satellite orbit 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. You collected coverage statistics using a Figure of Merit. Next you created a carpet plot to view how multiple parameters impact coverage. You used the optimization tool to scan through the design space to find a final solution that met your requirements.