Understanding Multidisciplinary Design Optimization

“Since the late 1950s, we’ve reduced fuel burn of airplanes per passenger-mile by over 80 percent,” says Joaquim Martins, a professor of Aerospace Engineering at University of Michigan. While more efficient engines get credit for a 50% savings, the balance comes from lighter, higher capacity, and more aerodynamic airframe designs.

When designing airframes, designers focus on two areas for improvements: the structure, and the shape. Because both of these areas are challenging to design and optimize, the typical design process has been to work on shape first, structural second, then bounce back and forth to refine and optimize. The problem with this process is that the two areas are not independent of each other. Change one, it alters the other. It’s hard to find the sweet spot that actually gives you the best overall design.

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The serial/iterative design process has worked well enough to provide a 30% improvement in fuel burn over the last 55 years or so, but gains are increasingly hard to make. And, even if simulation predicts that a design will be successful, it’s hard to know whether it’s optimal—whether, over the long haul, under all operating conditions, that design will provide the very best combination of efficiency, reliability, capacity, performance, and cost.

Multidisciplinary Design Optimization (MDO) holds the promise of transforming the design process, allowing designers to know, with some confidence, that the design they are creating—even if it is something with many conflicting requirements—is as close to optimal as practically possible.

MDO is an established technology, with a healthy ecosystem of commercial tool suppliers, strong academic support, and a pantheon of users, including a who’s who of aerospace and high-tech companies. It’s still considered by most people to be a back-end engineering tool. Something used by analysts and specialists to optimize individual parts or subsystems. Yet, its greatest potential value may be when it is used early in the design process, to optimize systems or products.

Recent research at the University of Michigan Multidisciplinary Design Optimization Laboratory provides a good example of this potential.

Beating Boeing at the fuel efficiency game
Dr. Joaquim Martins, along with PhD candidates Rhea Liem and Gaetan Kenway, recently published their research on the optimization of aircraft wings. In their paper, titled Multi-point, multi-mission, high-fidelity aerostructural optimization of a long-range aircraft configuration, they use the example of a Boeing 777, and show how an optimized wing design could cut the plane’s fuel burn, for all of its flights, by an average of 8.8% .

Consider that result for a moment: Boeing is no slouch when it comes designing wings to start with, so beating them by 8.8% is dramatic.

Wing design is an interesting case: the basic architecture of an airplane’s wing is usually established very early, during the conceptual design phase. The wing defines the essential characteristics of the airplane, and constrains many other design decisions. The thing that makes wings so hard to design is that their aerodynamics and structure are not just interdependent, they’re variable. “The wing is flexible, so even though you build it with a certain shape, it deflects and has many different shapes depending on the flight conditions, said Martins. “If you’re just doing aerodynamics, you’re not really considering that.”

Optimization of airplane wings is not a new concept. Some of the early research in this area dates back to 1977, when R.T. Haftka worked on the optimization of flexible wing structures subject to strength and induced drag constraints. Research has continued through the years, directed towards minimizing fuel burn.

The aim of Martins and his team’s research was to design a long-range aircraft configuration that was fuel-efficient in all expected flight conditions. Key to accomplishing this was the use of historical data on 100,000 Boeing 777 flights, from which they created a set of representative flight missions incorporating multiple flight conditions (e.g. takeoff, climb, cruise, descent, and landing.) This multi-point approach provided a more accurate profile of fuel burn compared to a single-point analysis considering only one flight condition.

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Some previous research on multi-point optimization of aircraft wings suffered from the use of 2D analysis or 3D analysis without aerostructural (simultaneous aerodynamic and structural) analysis, and the use of arbitrary weights to combine the operating conditions into a single objective. In this work, the researchers used 3D high-fidelity FEA and CFD analysis, enabling them to model the underlying physics more accurately and with fewer restrictive assumptions. And, by using historical mission data, they were able to determine the best weighting for a multi-point optimization, without resorting to guessing.

One of the significant factors holding back the widespread adoption of MDO is its computational cost. The use of high-fidelity models can raise the cost from merely expensive to unbearable. Parallelism is a lifesaver, but it can’t overcome computational inefficiency.

A good approach to gaining computational efficiency, which the Martins team used, is the surrogate model method. This involves using sampling to create a model (variously called a surrogate model, response surface model, or metamodel) that’s a “good-enough” representation of the high-fidelity discipline model within the expected range of conditions. The methods used to create surrogate models is a subject that only mathematicians could love. In this project, the researchers used the Kriging approximation, a statistical interpolation method that is popular in MDO.

Academic researchers tend to like to use academic (rather than commercial) CAE codes. For Euler CFD, the researchers used SUmb, a multi-block structured flow solver from the Stanford Center for Integrated Turbulence Simulations. For FEA, they used the Toolkit for the Analysis of Composite Structures (TACS) from the University of Toronto Institute for Aerospace Studies.

MDO professionals wax rhapsodic when talking about optimization methods. The simple rule you need to remember is that there is no perfect method. No method is guaranteed to find the global optimum for a general problem. Gradient methods can reliably find local optima, but may be unable to escape a local optimum. Stochastic methods will find a good solution, but it may not be the best solution. The Martins team chose the coupled adjoint method, which allowed them to efficiently compute gradients of functions with respect to hundreds of design variables. To implement this, they used SNOPT, an algorithm from Stanford.

The optimization model used a relatively coarse 1.2 million cell CFD mesh and a finite element model with 300,000 degrees of freedom. After completing the optimization, the analysis was re-run using a 2.1 million cell CFD mesh, to get more accurate results.

The optimization was run at SciNet, University of Toronto’s high performance computing facility, on a massively parallel supercomputer. It took 48 hours to complete 138 major iterations to get the optimal design.

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MDO is not just for aerospace
While this research, by Martins, Liem, and Kenway, was for academic purposes, the results are absolutely applicable to real world problems. Their choice of analysis methods, surrogate models, and optimization algorithms are a dead-on match for the methods used in commercial MDO applications.

MDO isn’t only applicable to big money aerospace applications. It can have a handsome payoff with more run-of the mill problems. If you want to investigate using MDO in your organization, you don’t necessarily need to use academic software tools. There are compelling commercial tools, with a dizzying range of capabilities. Here are just a few examples:

HEEDS, from Red Cedar Technologies, is an MDO application that connects to not only all of the heavy-hitter CAE tools, but also directly to SolidWorks and SolidWorks Simulation. It’s been used successfully in both very large, and very small optimization projects. For example, BD, a Fortune 500 manufacturer of medical technologies, used it to optimize the design of one of a next-generation syringe. They were able to identify a design that would result in a minimum assembly force and a maximum disassembly force. The design was unanimously chosen in a user study over a competitor’s design based on its performance, and has given BD a significant competitive advantage.

HyperStudy, a solver-neutral optimization program, is part of the HyperWorks enterprise CAE suite from Altair. Combined with Altair’s OptiStruct structural optimization program, HyperStudy offers multidisciplinary optimization of both geometry and topology. It has been particularly popular in the automotive industry.

ModeFRONTIER, from ESTECO, wraps around CAE tools, performing optimization by modifying input values, and analyzing outputs based on the objectives of the design problem. It also works in a 6 Sigma environment, by incorporating tolerances into the optimization process.

COMSOL Multiphysics includes an optional optimization module that can be used to solve shape, size, and topology optimization problems, inverse problems such as parameter estimation, as well as time-dependent sensitivity and optimization.

University of Michigan Multidisciplinary Design Optimization Laboratory
mdolab.engin.umich.edu

Red Cedar Technology
www.redcedartech.com

Altair HyperWorks
www.altairhyperworks.com

ESTECO modeFRONTIER
www.modefrontier.com

COMSOL
www.comsol.com

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