Probabilistic Problem Solving

probabilistic problem solving

Predictive technologies return uncertain answers—and that's the difference.

By Jean Thilmany, Associate Editor

Predictive technologies based on a probabilistic method of problem solving are gaining a steady foothold as a method of finding answers to engineering and other types of problems.

According to the developer of one such technology, these computer programs use mathematical models to predict the probability that something will or won't happen a particular way in the future. The tools can be used for design, sensitivity analysis, mathematical modeling of complex processes, uncertainty analysis, competitive analysis, and process optimization among other things, according to Mohammad Khalessi, who with Hong-Zong Lin co-founded a firm, Unipass, in Newport Beach, Calif., that makes predictive technology.

Khalessi developed technology of this sort as his dissertation, and continued development while he worked for Boeing in the late 1980s and early '90s. The aircraft manufacturer implemented his technology, and is still using it. In 1997, he and Lin formed their company. Other major organizations, notably NASA and several universities, are developing probabilistic technologies in-house.

The method differs from more traditional deterministic or statistical methodologies used to solve engineering problems, but it has some passionate backers who recommend its mathematical models to engineers.

The technology lets engineers create a model of the problem they want to examine, including variables, Khalessi said. For example, say that you wanted to figure out how much time to allow for the drive from your house to the airport.

Using the deterministic method, which forms the basis of many engineering analysis technologies, you would calculate determined values—the distance you need to go divided by the speed you'll be traveling—to figure out what time to leave. Once you've found that answer, you'd realize you need to allow yourself some extra time in case you hit traffic, had a flat tire on the way, or ran into other problems. You've found your answer, but you still need to allow for uncertainties you can't predict.

Predictive technology doesn't return exact answers. Instead, it delineates the probability of an event happening in a particular way.

Engineers less often use the statistical method of problem solving that ignores the time and speed variables, and focuses solely on statistical outcome. To apply that factor to our problem, you'd study a pool of drivers who took your route, find their average driving time, and allow yourself roughly that same amount of time.

"But there is really never enough statistical data available for doing something like that," Khalessi said.

He said that predictive technology combines both of these methods. "You start by creating a mathematical equation for what you want to do, then you look at each of the variables that you know or don't know and add it to the problem," he said.

To solve the time-to-the-airport example with predictive technology, you'd set up the problem: distance divided by speed equals the time it takes to drive from home to airport. You'd plug in distance and speed. But probabilistic techniques included in the technology allow you to account for variables you don't know, such as the driver's emotional state and possible wet or icy roads, as well as variables you do know, like speed or the ubiquitous presence of roadwork. You can plug in as many variables as you like because your answer isn't going to come back as a hard number; it's going to come back as a probable number.

The answer gives you the probability of getting to the airport in a specified time based on the variables you've entered. You could ask, "What is the probability, with all the variables defined, that I'd get to the airport in 45 minutes?" The technology might show you that 86 percent of the time making that trip you'd get to the airport that fast. You might then ask the probability of getting there in 30 minutes and be told you have only a 37 percent probability of arriving there on time.
Do you risk it? Do you leave 45 minutes before you need to be there? Fifty minutes?

The predictive technology outlines for you the risk factor involved in your problem. You have to decide how much time you want to allot based on that risk.

PREDICTING PART DESIGN

Engineers at the United Technologies Research Center in East Hartford, Conn., turned to a predictive technology two years ago after previously using the deterministic method of problem solving, said Wally Orisamolu, manager of the structural integrity and reliability group at the center, which carries out research and development for United Technologies.

"The key reason why we want to use this is to account for uncertainty," he said. "The idea is to capture and model those uncertainties as part of your predic-tion and to design processes so that you can still get the performance and durability of the product you expect, even under these conditions of uncertainty."

Just as in life, engineers face what Orisamolu termed huge amounts of uncertainty in carrying out their jobs. Deterministic tools are based on precise input and output (like speed, distance, or time in getting to an airport) and therefore can't account for variability in a model, he said. In the realm of probabilistic methodology it's okay not to know the precise input values. The reasoning goes something like this: Real life is variable and part life is variable, so predictions about these things need to be variable, too.

"If I asked you how much a particular object weighed, it would depend on how you measured it," Orisamolu said. "If you weighed yourself before and after Thanksgiving dinner, those numbers would be different. That's the same as variables in engineering design. There are so many things involved: load, how long the object will be used, and the accuracy of the model itself, too."

The predictive technology from Unipass has been used by the research center to design gas turbines, helicopters, and elevators.

"In each of these things we have structural components that are expected to carry loads during operation," Orisamolu said. "In gas turbine engines you have operational, mechanical, and thermal loads induced by the combustion process in the engine. That's how you get your power. You have all this and you're also subjecting your materials to a lot of punishment. You want to find out how long they'll perform successfully under these conditions and how long they'll last."

To determine how long a product will work before it breaks, Orisamolu's team programs the predictive technology to tell them the probability the part will run for, say, 20,000 cycles before it breaks.

"That's the shift of the design paradigm, right there," Orisamolu said.

Unipass technology allows users to create mathematical equations, plug in a number of variables, and find the probability of an answer.

By that, he means that this method of querying a technology about the probability a part can run for a set number of cycles changes the way an engineer designs. Instead of just determining if the part will work, the engineer can determine if he or she wants to design it in a particular way. If 20,000 cycles is an acceptable life for the machine and the probability is high it'll last that long, the engineer will go with the design. If the product needs a longer life, the engineer will change something to get it. The technology helps engineers produce robust designs because it accounts for the realities of everyday use on parts, Orisamolu said.

The ability to quantify risk is also important for engineers at the United Technologies research and development center. Using deterministic methods of finding answers, you can design a part that you think will work and that you think is safe, Orisamolu said.

"The probabilistic method is different because it defines the problem in terms of probability, which you can combine with the consequences of failure," he said.

To demonstrate, another example is useful. Say you want to cross a street, although there's a car coming toward you. You determine you have a 50 percent chance of making it across the street before the car hits you. If one of the consequences—or risks—in getting hit is death, you'd probably choose not to cross. Even though you have a 50 percent chance of living, crossing the street at that particular time won't be so important to you if you think you may die. But if the only risk in getting hit is that you might fall, get your pants dirty, and be embarrassed, you might choose to chance a trip across the street in the face of the approaching vehicle—even with a 50 percent change of getting hit. The consequences aren't nearly as high.

In other words, you know the odds of getting hit, but whether you play the odds depends on how much is at risk.

Because Orisamolu's group works with aircraft engines, they obviously have a keen interest in factoring risk into their models.

"If I look at an aircraft engine and say: 'What are the chances it could fail?' If the chances are one in a million but if it fails the aircraft could crash, I'm still not willing to accept that high a risk," Orisamolu said. "I'm not willing to accept one in a million. I want one in 10 billion. The consequence of failure is so high that I want the probability of failure to be zero, which isn't practical, but that's what I want."

Engineers at NASA—where the technique has some ardent backers—use technology based on the probabilistic method of problem solving.

However, if engineers have designed a component that is attached to the wing of the airplane and that won't cause major problems should it fail, they can accept a higher probability of failure. In other industries, risk factors might be looked at in terms of dollars. If a part failure will cost $10 million for a replacement, engineers might need a much lower probability of failure in the design they implement than if the part would cost only $10 to replace after it breaks.

By quantifying risk in this manner, engineers know if their designs are acceptable or unacceptable, not just that they will function as designed.

"In a deterministic method you can't accept a failure rate, because you don't know it," Orisamolu said.

Of course, the technology is not just useful for engineers. Khalessi sees a growing use in other industries that also use variables when making projections, such as insurance, real estate, and sales.

AREDENT FOR UNCERTAINTY

The probabilistic method and the newer predictive technologies that use it have some ardent backers. For instance, the probabilistic methods committee of the Society of Automotive Engineers states its mission as: to enable and facilitate rapid deployment of probabilistic technology to enhance the competitiveness of our industries by better, faster, greener, smarter, affordable, and reliable product development.

Lucas Horta, assistant branch head of the structural dynamics branch of the NASA Langley Research Center in Hampton, Va., uses the technology to predict structural response. Few tools allow uncertainty to be used when deciding whether or not to update a model, he said. Currently, the technology is his only tool to perform in-depth studies of parameter uncertainties, he said. The technology provides probability statements when engineers change the parameters of the problems they're working on, so they know how certain—or uncertain—they should feel about their designs, Horta said.

"I see predictive technologies use increasing exponentially in engineering and business applications in the next few years," Horta said. Practicing engineers will need to be retrained to understand the technology and what it can do for them, according to Horta. He predicted that retraining will be a factor in resistance to the technology.

"From a personal experience, I've approached people who were conducting experiments and offered to show them what probabilistic technologies could do for them," he said. "The reaction I get is, 'We have no need for it,' which just tells me they don't understand what this technology is all about."