It’s an Uncertain World

Brent Cullimore

You are hiking in the Serengeti. A twig snaps in bushes a few feet away from you. Is it the wind, or a lion?

As someone whose ancestors jumped to a worst-case conclusion (and as a result were less likely to become someone else’s lunch), we humans instinctively react with alarm in an uncertain situation. Fear of uncertainty is rarely warranted in the modern world, where stress hormones are more likely to shorten your life than to extend it.

Unless you are an engineer. We are taught to face up to uncertainty, right? Our job is to worry about gotchas; we design conservatively.

But something funny happens when we start to run numbers, especially if those numbers are produced by complex models solved by complex software behind the magic of a bright and friendly LED screen. We trust the numbers too much.

Many studies show that we subconsciously trust the recommendations of celebrities and other authorities, which is why you see them so often in commercials. As a purported human, I’m willing to admit that I am susceptible to that effect, even though the thought of Miley Cyrus influencing my decisions gives me the shivers. (OK, OK, so the effect only works for celebrities that you admire.)

Could it be that we anthropomorphize the computer and its program into an authority and trust it? (If you admire us or our software, thanks! But please don’t let that stop you from distrusting all initial results as a good engineer should.)

Or is it just too darned hard to consider the alternative? A messy world where even basic properties like the thermal conductivity of 6061-T6 aluminum have a few percentage points of uncertainty. A world where computer programs want fixed inputs and produce specific outputs. A world where managers just want a number and think that a large error bar just obscures a PowerPoint slide.

I would like to think that thermal engineers are more attuned to uncertainties than are other engineers. After all, we deal with some of the most uncertain characterizations out there: contact conductance, natural convection film coefficients, and so forth. I can say that since you’re probably a thermal engineer if you’re reading this, and hey, I’m not above pandering.

The math for handling uncertainties isn’t hard to learn or apply. However, we are rarely taught to use it in schools, except for measurement uncertainties and design drawing tolerances (where the concern is geometric rather than analytic).

We first introduced a Reliability Engineering (aka stochastic analysis) module in our software over 20 years ago. More importantly, at about the same time we made it possible for almost every value to be input not just as a value, but also as an easily varied parameter. We offered scaling factors throughout the programs, and we have continued to design new features along the same lines. A question such as “What if this input is off by 50%?” is easy to address, as are “What is the worst-case conditions I should design to?” and “What is the best-guess value for this uncertain parameter, given this test result?”

from: Advanced Design Modules

Other CAE software vendors have similarly addressed a need for statistical design capabilities (e.g., ANSYS' More Certainty by Using Uncertainties.pdf,  and CD-Adapco's Robust System Design Simulation). But you just don’t see these capabilities front and center, and it is no wonder: the demand is low. When we offer seminars on this subject, they are slow to fill.

Given the huge uncertainties involved, and our need to design conservatively, and the ease with which these uncertainties can be addressed, why aren’t those the most popular seminars? I am at risk of being a hypocrite myself: few of my own models include adequate investigation of uncertainties. Why is that?

One important reason is that there is an infrastructural gap. Tables of conductivities, K-factors, and insulation performance almost never show min/max values much less standard deviations. Development contracts always state performance requirements, but are often missing required probabilities of success associated with those requirements.

I can hope that the dearth of data on uncertainties will be addressed someday. That all design software will respect uncertainties. That all engineering students will leave the university with a healthy knowledge of the limits of certainty. And that all managers will learn to love error bars.

Until then, may the uncertainties in the dark branches of your thermal model be wind, and not lions.