Surrogates Promise Better, Faster Designs
Using an approximation model is often the best way to address a challenging problem or to accelerate a lengthy process.
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January 1, 2012
By John Edwards
Experiments and simulations lie at the heart of a wide range of engineering design projects. From creating aerodynamic vehicles to pinpointing the best place on a wing to place an aircraft engine, experiments and/or simulations are used to isolate design objectives and constraints. There’s a down side, however: Experiments and simulations are both time-consuming and costly.
One way of reducing the burden is by building approximation models, otherwise known as surrogate models.
Surrogate modeling’s roots trace back several decades to the mining industry (minerals, not data), says Dr. Andr s S bester, a lecturer at the University of Southampton’s School of Engineering Sciences in England, and co-author of Engineering Design via Surrogate Modeling: A Practical Guide (Wiley, 2008). The goal in a mining environment is to find the location containing the highest ore grade using the minimum amount of test drilling.
To achieve this goal, engineers created a three-dimensional surrogate model of the ore grade function, based on a few known concentration values.
“A whole new science—geostatistics—developed around the question of how to do this most efficiently,” Sobester says.
Design engineering, beginning with the automotive and aerospace sectors, picked up many of the formulations developed for geostatistics.
“Oddly, it works much better in these fields than in mining, as most of our functions are continuous and smooth—ore grade variations are not,” Sobester says.
Quality on the Quick
Sobester observes that surrogate modeling is all about reducing time and cost without sacrificing accuracy.
“It allows you to make the most of your experiments, whether they are numerical or physical,” he says. “In essence, if you can only afford to measure the performance of a parametrically defined product in a few points in the design space, it gives you a statistical estimate—complete with error bars—of what the performance is at untested locations.”
In desktop engineering, the surrogate “killer app” is design optimization, Sobester says. Say, for example, that your parametric design has five variables. You can only afford to simulate the performance of 15 instances—15 sets of five variables. Conventional, so-called “direct” optimizers have little chance of getting anywhere in 15 evaluations, he notes—but a surrogate model might.
“A surrogate model of a 5d function based on 15 points may not be terribly accurate, but it will give you a good idea of the most promising region of the design space,” he says. Plus, he adds, “You can search the surrogate to your heart’s content (with direct optimizers), as its computational cost is negligible.”
More designers are turning to surrogate models to meet the accelerating development timeframes demanded by real-world business demands.
“We have recently completed a study supported by the Royal Academy of Engineering, looking into the acoustic and aerodynamic performance of an unusual engine installation geometry for passenger airliners,” Sobester says. The designers placed the engines on pylons on top of the wings, to use the wings as noise shields between the engines and communities on the ground.
“We could test the acoustic performance of about 40 different designs via experiments conducted in the University of Southampton Large Anechoic Facility,” Sobester notes. “At the same time, we were able to run a similar number of high-fidelity computational simulations of the airflow around the aircraft.”
By fitting a surrogate model to each dataset, the designers were able to locate the best trade-offs between noise shielding performance and aerodynamic performance—many of these designs being at untested points. “But at points where the surrogate had low error margins,” Sobester points out.
Sobester notes that wider surrogate modeling adoption has been blocked by a potential for ambiguity that has deterred many designers.
“Some of the mathematical apparatus behind surrogate modeling is actually quite complex, and it makes some assumptions regarding the underlying objective function we are trying to model,” he says. “I think it took engineers a while to realize that, although we can almost never be certain that our objective functions do not violate these assumptions.”
He notes that in practice, however, this rarely matters. “After all, if you have 10 shots at a five-dimensional function whose optimum you seek, you are not going to lose sleep over whether it is continuous for any ‘x.’ Surrogate modeling is the only weapon you have, so you might as well use it.”
A Tool, Not a Shortcut
Designers must take care not to view surrogate modeling as a quick and easy shortcut, Sobester warns. While the approach can save time and effort, care must still be taken to ensure that all the pieces are in place for quality results.
“Like any sharp tool, (surrogate modeling) has to be treated with some caution,” he says, noting that surrogate model formulations often have a large number of parameters that must be “trained” to the data at hand.
“This process requires some care, in particular when the response being fitted is corrupted by noise—numerical or experimental,” Sobester says. “An incorrectly trained model can be seriously misleading.”
Just about any designer can become reasonably proficient in surrogate modeling without going back to school or neglecting current work obligations, however. In fact, Sobester’s journey started with a pair of papers by Dr. Don Jones, a mathematician working for General Motors, that were “easy to follow, yet based on solid foundations.”
Sobester also recommends reading an introductory textbook on the topic that “will highlight some of the main pitfalls, without going too deeply into the statistical subtleties.” Perhaps the best way to get started with surrogate modeling, however, is by practicing the technique.
“Depending on your favorite way of interacting with a computer, there are a number of tools available,” Sobester says. “For the tinkerer who likes to customize a code to their own specific application, there are some decent Matlab codes out there.”
Meanwhile, designers who prefer a graphical interface and a higher-level approach will be glad to know that most of the big design process integration tools now have a surrogate modeling facility.
Sobester sees a bright future for surrogate modeling, although he says he believes that the approach must undergo some changes to make it more appealing to a wider number of designers.
“If this technology is to be fully embraced by industry, it has to be made user-friendly without sacrificing too much mathematical rigor,” he says. “This is a challenge that will have to be addressed.”
Increased computational efficiency should help bring surrogate modeling more deeply into the design mainstream, he says, by making the necessary software tools easier to use and faster while reducing overhead costs.
“While querying surrogate models, once built, is usually very cheap, their actual construction process can be computationally expensive at the moment, especially for large training data sets,” Sobester concludes.
Another Role for Surrogates Just as surrogate modeling can eliminate or reduce the need for expensive and time-consuming experiments and simulations, surrogates can also be used to make desktop design software more flexible and easier to use. Dr. Niklas Elmqvist, a Purdue University assistant professor of electrical and computer engineering, says that “surrogate interaction,” a term he and his fellow researchers recently coined, could lead to a new generation of intuitive desktop design software. In a surrogate interaction design environment, surrogates are used to present interactive graphical representations of real objects, with icons on the side labeling specific parts of the figure. Elmqvist notes that while many design software developers have already incorporated surrogate interaction approaches into their products, the concept has so far evolved on a piecemeal, ad hoc basis. He maintains that a formal definition of what surrogate interaction is, and how it should be used, would help speed its development and refinement—while expanding the number of applications using the approach. “Design tools incorporating surrogate interaction have the potential to greatly simplify everyday design tasks,” Elmqvist says. “Conventional computer-aided design (CAD) applications typically rely on the use of scores of menus with hundreds of selection options.” Surrogate interaction, on the other hand, generates images that aim to mimic real objects, giving users a helpful, intuitive interface instead of a series of confusing menus and selections. Elmqvist says that working on a design in a surrogate interaction design environment is almost like tinkering with the actual object. Elmqvist says surrogate modeling will make life easier and more pleasant for designers, while shortening the time needed to accomplish specific tasks and, ultimately, slash project costs. “It changes the way designers work,” he says. On a car design, for example, one could easily and intuitively change the placement of the wheels, the doors, the antenna, etc. “As things exist now, I can’t make those changes to the drawing directly, but have to scroll through a bunch of menus or use arcane commands,” Elmqvist says. Elmqvist notes that while design software makers have strived over the years to make their products more intuitive and interactive, the results have been mixed. A big drawback, Elmqvist says, is that designers must learn new rules every time they switch to another developer’s software—or sometimes, even products within a particular vendor’s line. “There’s currently no coherent underlying principle,” he says. “We want the surrogate interaction concept to unify all of the other techniques that have been created over the years.” |
John Edwards is a technology writer based in Gilbert, AZ. His work has appeared in IEEE Signal Processing, Electronic Design and other publications. Contact him at [email protected].
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