Sensitivity Analysis with MATLAB for Student Competitions - MATLAB & Simulink
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      Sensitivity Analysis with MATLAB for Student Competitions

      From the series: Aerospace

      Khushin and Connell present the MATLAB® code for sensitivity analysis for student competitions, available on the MathWorks® GitHub® repository and File Exchange. They discuss the AIAA Design/Build/Fly 2021 competition mission score as a case study and identify the most sensitive design variables to maximize this competition score. You can easily modify the code to fit your requirements and adapt it to determine appropriate design choices to maximize your competition score.

      They begin with an overview of sensitivity analysis and its significance in aerospace design competitions. Sensitivity analysis (SA) is a technique employed to gauge the impact of uncertainties in input variables on output variables within a model. In the domain of engineering design, sensitivity analysis is utilized to pinpoint the most sensitive design variables to optimize the design space.

      Proceeding further, they delve into the competition score as a case study, scrutinizing various mission scores and identifying the most sensitive design variables across all missions to optimize the mission score.

      Published: 20 Dec 2023

      Hello, everyone. Welcome to another video in the Aerospace Student Tutorials and Video Series. Joining me today I've got our new aerospace student programs technical lead, Khushin Lakhara, who works in our Bangalore office. Hello, Khushin. Welcome to your first video for the Aerospace Series.

      Thanks a lot, Connell.

      So Khushin, why don't you go ahead and tell us a little bit about yourself and why you'd be the best person to talk about aerospace student content for us?

      Thanks, Connell. So as you introduced, I'm working with the student programs team. And I support the aerospace competitions globally, so I have been interacting with the student competition teams worldwide. And I found out how they have been doing.

      And even when I was the student I was also involved in such competitions, and also, the aircraft design and flight controls are two of my major area of interest. So I have been trying my hands on the multiple tools, and finally, I come up with something which the teams require.

      Awesome. So today's question is going to help us understand what sensitivity analysis is for aeromodeling competition. Now, sensitivity analysis at a high level is essentially trying to-- it's one of the first design steps that you take as a team that's building model airplanes, so without wasting too much time, let's jump right into our topic for today. Khushin, the floor is all yours.

      Thanks, Connell. So today, we are going to discuss about the sensitivity analysis, and our discussion would be especially around the aeromodeling competition, so first, we'll be starting our discussion with the understanding what is sensitivity analysis. Once we understand the sensitivity analysis, we will be exploring why is it important for aeromodeling competitions, and we will be also taking a case study which is based on the AIAA Design/Build/Flight 2021 competition score problem.

      And we will be solving this problem using the MATLAB, so we'll be having a software demonstration. And after that, we will be concluding with some of the key takeaways, and we'll explore that how sensitivity analysis can help us to take a better design decision so that we can maximize our score for the competition.

      Awesome. So without wasting too much time, let's learn what sensitivity analysis is.

      So sensitivity analysis is basically a study to measure the impact of uncertainties in input on output variables of a model. It also helps to determine most sensitive input variable and the range of input variable input values where model will be most sensitive. By getting this understanding, we can actually design our aircraft or design our system in such a way which gives us the best possible score.

      The sensitivity analysis is done with the multiple methods, but mostly it's performed with the univariate, multivariate, and local and global methods. Today, we are going to keep our discussion around the univariate sensitivity analysis, and we'll be exploring the design space with this. So let's move forward and understand why this sensitivity analysis is important for aeromodeling competitions.

      Mostly in the aeromodeling competition we see that organizers gives us the conflict for design requirements, and as the team wants to maximize their score, so lots of confusion are there that, OK, which design space should we choose? So sensitivity analysis actually helps us to identify the most sensitive design variable for a given scoring formula. It also helps us to make the better design decisions among the conflicting mission requirements, and finally, it helps us to optimize the aircraft design for a better score.

      Yeah, I can see-- I can see how this is important for a complex system like an aircraft where everything is coupled together. You increase the size of your wing. You got to increase-- there are going to be corresponding changes in fuselage length, for example, just to make sure that your aircraft is stable.

      So yeah, I can see how having to programmatically or mathematically, essentially, check how much one change-- how much a change in one particular design variable affects something in the others. I can see how this can help you get started.

      Yes, yes. So we are going to discuss the same with our case study. So we are having this case study of AIAA Design/Build/Fly competition of 2021. So in this competition, teams need to fly for this course layout, and they had the multiple missions. So in mission one, it was binary, where they need to make a successful flight, so if they are making a successful flight, it would be 1, else they would be scoring 0.

      In mission two, they had two design variables, and those design variables-- or those score formula was actually the comparative to the best team. Similarly, for the mission three, also, they need to score or need to-- or need to score a relative score to the best team, and there were total three design variables. So number of laps, sensor length, flight time. So in this competition, actually, the teams need to tow a number of sensors, a number of sensors as payload, payload for the complete mission.

      And finally, they had the ground mission, so ground mission was-- again, it depends on the crew's skills, and it was just to load and unload the payload in the mission. So total mission score was the sum of all.

      So yeah, so just off the looks of it, it kind of seems like a very-- it seems like very conflicting scores because on one hand, you're measured for flight time. You always want a lighter or a smaller aircraft. You want to fly faster. But then you're also getting points for actually carrying more payloads and carrying more sensors, so that automatically means a heavier aircraft. So I can see these are very sort of antithetical missions, if you will.

      Yes, Connell. You took it right. Actually, the problem the teams face is to choose between a faster aircraft or a heavier aircraft. And we will be exploring through our demonstration that, OK, should we choose a faster or heavier aircraft? So just let's quickly move to our software demonstration, and we'll explore it from there.

      To perform the sensitivity analysis, we have developed a MATLAB live script. In this script, we will be exploring about the multiple mission scores and identify which design variables are most sensitive. So we start-- we start our work with the score-- with mathematically formulating the mission scores.

      As we see this in the mission scores, the relative scores are there for mission two and mission three, so we need to take a best score, our best team's score. So depending on the previous-year reports, we have come up with the performance for best team, and we actually modeled all the parameters of the best team.

      And then we are identifying that, OK, what team is the best team? So just to start, we are assigning our team variables to the best team variables. Moving forward, all the mathematical formula or mathematical formulas for the scores has been modified. Once we are ready with the-- ready with this, we have actually introduced the change variable.

      This change variable will help us to introduce the change in the various design variables. We are starting from minus 50 and will be-- minus 50%, and we will be going up to the plus 50%. We will be seeing how the change of each design variable is making impact on the total mission score. So we have performed this sensitivity analysis first on three missions, on the mission two score, mission three score, and ground mission score.

      So here we see-- here we see this beautiful plot which shows that, OK, all three curves has the positive slope, so positive slopes means the direct or proportional relation with the variable. So if my input variable is changed or design variable is changed, it will be directly impacting the mission score. Mission three is the most sensitive mission, followed by mission two, and the ground mission is the one which is the least sensitive mission.

      And as the ground mission involves the loading and unloading of the-- loading and unloading of the payload and it depends highly on the crew's skills, so we can neglect this for our future analysis. But mission two and mission three score has the multiple design variables. So mission two has two design variables-- those are sensor flight time-- and mission three has three design variables, which are number of laps, sensor length, and the sensor weight. So now the question is, which one is the most sensitive design variables?

      So if we can go back to that plot real quick, essentially what that plot is saying is, depending on how steep the slope is, that's the particular score that is most sensitive to our problem, right?

      Yes.

      Is that a fair assessment? OK. Cool.

      Let's quickly explore the mission two score. So to perform the sensitivity analysis on mission two score, we are defining an array, which is the flight time array. So we are waiting here the flight time for from the best team's flight time to the higher limit, which we have considered as 200 seconds. So in this flight time we are waiting and will be plotting the impact of the flight time and the number of sensors here.

      So we also define another array, which is for the sensor, and then we plot both of-- the effect of both the variables on the total mission score. Here we see that mission to score-- mission to score has the curves with the negative slope, which means the mission two score has indirect relation or reciprocal relation with the total time, which is actually expected, that lesser the flight time is there, the higher would be the mission score.

      But another point to identify here is that once we increase the number of sensor, the slopes of the curves started increasing, which actually gives us the understanding that, compared to the flight time, the number of sensors or the payload is the-- so payload is the most sensitive variable and which is making a more impact on the mission two score.

      So here we can make some inferences that, OK, as the number of sensors are most sensitive to mission two score than flight time, so heavier aircraft would be-- heavier aircraft would be a better choice compared to going for a faster aircraft. But if our heavier aircraft gets-- if somehow we can make our heavier aircraft fast enough, then we'll be scoring more.

      So with this understanding of mission two score, we'll be moving now to mission three score. In the mission three, we do have three design variables, which are sensor weight, sensor length, and the number of laps. So we'll be comparing those three variables against each other, and we'll be seeing their impact on the mission three score.

      So let's start with the discussion on number of laps and sensor weight. So again I define here an array, which is going from a 0 sensor weight to the highest sensor weight, which was carried by the best team, and then we are introducing the number of laps array as well and performing-- and then calculating the mission three score.

      And we plot it here. Here we again see that we do have a positive slopes of the curve for the mission three, so that means sensor weight is directly proportional to the mission three score, which is expected, that, OK, the more the payload you carry, the higher the score you will-- higher the score will be. Also, we identify here that as we are increasing the number of laps-- as we are increasing the number of laps-- that means the lesser flight time-- the score is getting-- score is increasing sharply.

      So in that case, we can actually inference from here that the heavier aircraft is desired, but if your heavier aircraft, again, gets faster, you will score more. And that's what we explore-- that's what we explored in the last mission as well. So again, we are here with the same understanding, so now let's move to another correlation study, which is on the number of laps and sensor length.

      So here again we are introducing a variable, sensor length array. Here we have taken the minimum sensor length, which was given by the competition organizers as a requirement, and we are taking to the highest sensor length, which was carried-- which can be carried by a best team, introducing them, and again recalculating the mission three score analysis with this.

      And varying the number of laps, we come up with this plot, which shows that, OK, sensor length is also directly proportional to the mission three score, and more the number of laps, the higher the score, which is expected that, OK, the longer your sensor is, it may be more heavy. And it's more heavy, you will be scoring more. So here this mission tells-- and the study tells that if you have a longer sensor-- it means a longer fuselage-- or heavier aircraft, that may result more. So that may result in a better score, so heavier aircraft is again in demand.

      Moving forward to the last correlation study, which is in the-- which is between the sensor length and sensor weight-- so here we have actually capped our number of laps as a constant, and then we have introduced-- we have introduced the array between sensor length and sensor weight, so we are using here the meshgrid.

      So instead of just plotting the curves, we are coming up with a surface here, and once we do it, we see this beautiful plot, beautiful 3D plot here, which is giving an understanding that, OK, if I do have a lesser-- or if I do have a smaller sensor, a smaller sensor and a lighter sensor, I would be scoring less, but if I'm increasing both of them, my mission three score will be going up.

      So here also we get an understanding that, OK, one should carry a heavier and longer sensor. But there are multiple parameters we discussed here, and we need to find which one is the most sensitive design variable. So now we will quickly move to the slides, and we'll bring all our conclusion there and try-- from there, we will try to take a final design decision.

      So just to recap our total sensitivity analysis study, we started our study with studying the various missions, so we found that mission three was most sensitive, followed by mission two. And then the ground mission was there. In the design variables also, we did have-- also, we have two variables in mission two and three design variables in mission three.

      So the question is, which one is the most sensitive design variables? So let's quickly compare all the results and see which one is the most sensitive design variable. So in mission two, we saw that slopes are negative, hence flight time impacts inversely. So a lighter and faster aircraft would be less sensitive compared to a heavier aircraft, and a heavier aircraft will be scoring more on getting faster, which we saw in the plots.

      So here in this mission two, we found out that, OK, the sensors, number of sensors, is the most sensitive parameter compared to the flight time, so number of sensor will actually lead to the heavier aircraft or the heavier payload. In the mission three score analysis, where we had three studies-- so in the three studies, we saw that in the first one the sensor weight would be the most sensitive compared to the laps.

      In the second study, we saw that sensor length would be the most sensitive, and in the third one, we saw that sensor weight would be the most sensitive parameters. So when we compare all three studies, we find that, OK, sensor weight is the most-- sensor weight is the most sensitive followed by sensor length and finally, the flight time.

      Now, comparing the mission two and mission three together, if we see, the mission three was most sensitive. Mission two was less sensitive. But if we look in all three parameters, sensor weight has been the most sensitive design-- the most sensitive design variable. So we can take the design decisions from here that a heavier aircraft will be required compared to a lighter and faster aircraft, a longer sensor payload will be scoring higher compared to the smaller sensor.

      And that's where we go to the key takeaways. So we saw in our discussion that sensitivity analysis helps to identify design variables with the most impact on the mission score, and we also explored how the MATLAB capabilities helps us to visualize the design space and explore impact of various design variables.

      Awesome. Well, thank you so much, Khushin. I think I-- I think it opened my eyes a lot more to how-- when you go to think of it, none of those-- none of those design-- all of those design variables were-- what we call design variables were essentially variables made up by the competition, and it's very interesting to see how-- this is the first step of your design, right?

      This is-- before you start any calculations, you want to say, OK, what am I designing my airplane around? Am I designing it to be lighter? Am I designing it to be faster? Or am I designing it to be heavier and carry a lot more payload? I think this makes a lot of sense as to why-- I remember going to the competition in 2021, and the planes were huge. They could carry a lot of weight.

      So I think that makes a lot of sense. So hopefully, to our audience out there, this helps you all get started with designing aircraft in MATLAB. But Khushin, thank you so much for taking the time to come and talk to us. I'm going to leave you guys with some resources that you can use to get started with using MATLAB and Simulink.

      Remember, we offer complimentary licenses to everyone taking part in AIAA Design/Build/Fly as well as SAE AeroDesign. So if you're taking on one of those competitions and need to get access to MATLAB, you can use the link on the screen to reach out to us, and we'll help get you set up.

      But there are also a number of resources, some more videos and blogs that you can take a look at. But please, let us know what you'd like to hear more from us about, and we'd be happy to make some more content for you. Thank you so much, and we hope to see you again on this video series.

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