Navigating Uncertainty – Arriving at the Signal in the Noise

This article first appeared in the November 2014 Flight Test News.

What is a Markov chain Monte Carlo model, and why does it matter? What is the difference between RNAV and RNP? What is a data band? How is it different than tolerance? Why do we use them? 

These are all significant questions, and their answer hides like a valley masked by the long shadows of towering mountains. These peaks grab our attention. They are a more familiar sight like the primary disciplines of flight test engineering—performance, flying qualities, test conduct, and systems evaluations.  But in the misty fog-filled valleys below, data flow like a mountain brook. Downstream we are drowning in data.  

The challenge for flight test in the twenty-first century is to build a dam to control the flow of data, like we control the flow of water—transform the flow of data into insight and information, just as we transform the flow of water into hydroelectric power. As flight test professionals, we must adapt to the evolving nature and quantity of flight test data. We must begin to familiarize ourselves with a more diverse array of applied tools of mathematics and statistics, building blocks to understanding data and using it to make decisions. Expert application of these tools is critical if we will successfully navigate the uncertainty and find the signal in the noise.  Noise – this is the most common statistical phenomena in flight test, and understanding it better is the goal of the second half of this discussion, an objective to which we will return. This discussion, though, is just part of a larger strategic discussion—one that has been conducted rigorously, among other places, in the break room and cubicles of the flight test department at Honda Aircraft Company. It includes the following points:

1. Probability is as important as airmanship;
2. The important thing is not (necessarily) the formula for standard deviation or any probability distribution but the big ideas, the fundamental principles and the way our knowledge of them guides our thinking; and
3. We need to communicate a clear and convincing explanation for flight test professionals in some format less than dissertation length. 

Would you mind reading the following anecdote and letting me know if a light bulb comes on for you? Does this story motivate and correlate to these fundamental points?

I want you to recall an elementary idea, a cross-country flight. Do you remember back to the days when you were learning how to fly? For me, the plane was a Cessna 152, tail number four-hotel-bravo, and the place was Cook County Airport (15J) in southern Georgia.  My instructor’s name was Ian. He flew seaplanes somewhere in the South Pacific for many years before teaching private pilot students.

When I walked into the flight school one day, Ian told me something I would never forget.  In fact, he predicted I would never forget it before he even told me: “Can ducks make vertical turns with turbulence.” That mnemonic helps me remember the steps needed to plan a cross-country flight. The fact is, a pilot’s head is full of crazy sayings and silly words that mean something when translated into aviation jargon.  Remembering a wacky sentence about ducks is easier than remembering Compass heading, Deviation, Magnetic heading, Variance, True heading, Wind correction, and True course. Back at Cook County Airport, I opened up the sectional charts and sat down to figure out where I wanted to go. Once I did, I could draw a single straight line on my chart and jot down a heading.  Those two things would get me pretty close: 255° magnetic for 25 minutes. After five minutes on a 255° heading, I should cross over a major highway with an overpass to my left. I look outside to see where it is. It’s not as far south as I thought it would be. At seven-and-a-half minutes, I should pass over the southern tip of a large pond. The pond is just north of my position.  Apparently, the winds are drifting me south of my intended course. I correct my heading to 260°. At 15 minutes, I should overfly an intersection in a small town. I am just north of the intersection. A heading of 260° corrected me back to course and then a bit right. Two-five-seven is right in between. That should keep me on course. 

Three steps—clock to map to ground—are the process we follow when navigating in an aircraft. There is this notion, “the pond is just north of my position.” Being able to recognize that and make that judgment call is a critical element of airmanship.  It’s also a fundamental principle of applied tools of mathematics and statistics. Sometimes, “just north of my position,” is close enough. In this case, we don’t need to quantify what “just north of” means. 

In summary, I want to explicitly state three fundamental facts.

1. We are going to encounter uncertainty—uncertainty means we won’t hit every waypoint.
2. Predict-test-evaluate is the process for navigating uncertainty. In aviation, this means plan the flight— fly the plan using the “Clock-map-ground” technique—and evaluate, using your “engineering judgment,” when that’s close enough.
3. Applied tools of mathematics and statistics help us evaluate when “that’s close enough” (as in the case of navigation above) or when more quantitative rigor is needed.

The Rest of the Story

At the beginning of this column, I promised to return to the subject of noise, the most common statistical phenomena in flight test. Henceforth, this is the subject of our discussion and a beta test of what I hope will be an evolution in the math section of the SFTE Reference Handbook.

This article first appeared in the November 2014 Flight Test News.

Related: Introduction to Measurement Error.

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