The path toward certification by simulation, Part 2: UQ lessons from NNSA

Dr. Mark Anderson is Technical Advisor to the National Nuclear Security Administration (NNSA) within the U.S. Department of Energy (DOE, Washington, D.C.). “We started looking at simulation-based certification about 15 to 20 years ago, and what would be required to achieve that,” he says. “The Verification & Validation (V&V) subprogram is a critical part of the roadmap we established to reach that goal. However, we are not there yet. We still are not certifying serious modifications to old designs and releasing those into the nuclear stockpile. We are probably still about 10 years away due to some unique issues.”

He gives an example that for some of the nuclear materials even small-scale experiments are extremely expensive. “So this has led us to the concept of developing very robust designs that take into account the uncertainties we have yet to resolve and then over time we will be able to build confidence and back off of the overdesign.”

I respond that the aerocomposites industry also seeks to move away from its traditional “overdesign”. Anderson replies, “Yes, but this is not robustness. Traditional design uses deterministic design variables and safety factors to account for unknown and unquantified uncertainties, resulting in overly conservative designs. Robust design directly models uncertainty in the design variables using probability density functions, thus producing designs that are less conservative by putting 'boundaries' on the uncertainties.” He notes, however, that this requires techniques to propagate the uncertainties through the models.

“UQ actually gives you a great language for pursuing optimization,” says Anderson. “You propagate the parametric uncertainties through the model by varying all of the parameters (e.g. material, boundary conditions, loads, geometries) and then re-running the simulation so that you develop a set of data to which you can apply probability density function analysis. In parallel, you attack the model form uncertainty by using small-scale experimentation to verify and refine the model. Thus, you are not getting away from experiments, but hopefully you are reducing the number of more costly, large-scale tests required by investing more in the front end via model development and small-scale tests.”

What part do science-based and multi-scale models play in all of this? “Although there is a lot of theory that has gone into the models that have been developed in the composites industry,” replies Anderson, “many are still very empirically based. In other words, they use a simple mathematical description that fits to empirical test data. The alternative is to develop a science-based model at a microscopic level that predicts well empirical data, but also is then scaled up to a macroscopic level.

This is an area of research that is receiving increased attention. We have had pretty good success in developing multi-scale models in NNSA that predict well from nano-scale atom level up to continuum level. This may be possible in composites, but not necessarily always practical. For some types of materials and structures, it may be more cost-effective to test. There is not one single recipe you can apply to multi-scale modeling. It differs by industry and problem trying to be solved. However, in principle it is an engineering concept that can offer efficiency in design and development.”

Anderson describes NNSA’s roadmap in developing the V&V technology it required, "The basic goal is to make sure that the models are as accurate as possible in their predictive capability. One part of this was to use academic institutions to help develop the science-based models and multi-scale modeling capability. Since 1997, we have had several rounds where five universities are selected to participate for 5-year programs.” The last round ended in 2013. Shortly thereafter, the next round of selections were being finalized. “When we invest in the universities [$17 million per university for the 5-year period, totaling $85 million for this part of the V&V program], we contractually require them to fit the V&V program vs. their own research format. For the area they are contracted — for example, Cal. Tech. is the center for Predictive Modeling and Simulation of High-Energy Density Dynamic Response of Materials — they must pursue a balance of simulation and experimentation and demonstrate their approach in comparing the two." Anderson continues, "Also, at the end of the program, they must make a prediction in their area quantifying the uncertainties. We visit them a couple of times per year and then they make an end of program presentation and final report. This is how we have developed the science-based models that we use.”

Can the composites industry follow the NNSA model? Anderson says it is possible, but it may not be practical. “For most industries, what would be most appropriate is a balance between the historical testing-based approach and this simulation/UQ-based approach. I don’t believe the aerospace composites industry will want to qualify a new material for an aircraft fuselage without testing. However, by investing money into building simulation capability, it will be possible to reduce the cost of testing from, say $500,000 to $100,000, for example." Regarding the actual structure of a program to develop this simulation capability, Anderson says simply, “The composites industry will have to work out what makes the most sense for it to achieve its goals cost-effectively.”

He adds one last note, “We (Los Alamos National Laboratory) are pursuing an alternative UQ approach not directly tied to the parametric/model form/test uncertainty paradigm because that paradigm can lead you astray in many situations, even if done properly. For now, we are calling it simply ‘physical uncertainty bounds’.”