“100% digitally designed using 3D solids technology”
Boeing invested more than $1 Billion (and insiders say much more) in CAD infrastructure for the design of the Boeing 777. Boeing based their CAD system on CATIA (short for Computer-Aided Three-dimensional Interactive Application) and ELFINI (Finite Element Analysis System), both developed by Dassault Systemes of France and licensed in the United States through IBM. Designers also use EPIC (Electronic Preassembly Integration on CATIA)and other digital preassembly applications developed by Boeing. Much of the same technology was used on the B-2 program.
While the marketing hype has certainly distorted the picture, the reality nonetheless is that Boeing reaped huge benefits from design automation. The more than 3 million parts were represented in an integrated database that allowed designers to do a complete 3D virtual mock-up of the vehicle. They could investigate assembly interfaces and maintainability using spatial visualizations of the aircraft components to develop integrated parts lists and detailed manufacturing process and layouts to support final assembly. The consequences were dramatic. In comparing with extrapolations from earlier aircraft designs such as those for the 757 and 767, Boeing achieved
While the Boeing 777 experience is exciting for the VE enterprise, we should recognize just how limited the existing CAD tools are. They deal only with static solid modeling and static interconnection, and not—or at least not systematically—with dynamics, nonlinearities, or heterogeneity. The virtual parts in the CATIA system are simply 3D solids with no dynamics and none of the dynamic attributes of the physical parts. For example, all the electronics and hydraulics had to be separately simulated, and while these too benefited from CAD tools, they are not integrated with the 3D solid modeling tools. A complete working physical prototype of the internal dynamics of the vehicle was still constructed, a so-called “iron-bird” including essentially everything in the full 777.
While there was finite element modeling of static stresses and loads, all dynamical modeling of actual flight, including aerodynamics and structures was done with “conventional” CFD and flight simulation, again with essentially no connection to the 3D solid modeling. Thus while each of these separate modeling efforts benefited from the separate CAD tools available in their specialized domains, this is far from the highly integrated VE environment that is envisioned for the future, and is indeed far from even some of the popular images of the current practice. Thus while a deeper understanding of the 777 does nothing to reduce our respect for the enormous achievements in advancing VE technology or dampen enthusiasm for the trends the 777 represents, it does make clear the even greater challenges that lie ahead.
What are the next steps in CAD for projects like the 777? Broadly speaking, it involves much higher levels of integration of the design process, both laterally across the various subsystems, and longitudinally from preliminary design, through testing, manufacturing, and maintenance. It will require more systematic and sophisticated treatment of uncertainties, even in the solid modeling, but even more critically when dynamics are considered in a unified way. This will of course lead to nonlinearities and heterogeneity and the need for variable resolution models.
Boeing engineers view these steps as enormous challenges, but ones that must be faced. Even something as simple-sounding as using the CATIA database describing the 3D layout of the hydraulics and their interconnections as a basis for a dynamic simulation of the hydraulics remains an open research problem, let alone using CATIA as a basis for dynamic modeling and simulation of aerodynamics and structures. What is difficult to appreciate is how the sheer scale of keeping track of millions of components can be computationally and conceptually overwhelming.
To illustrate some of the
issues in the 3D solid modeling for the 777, we will consider yet another extremely simple
cartoon experiment (although the main motivation for introducing these ideas now is to
draw broader analogies later) in 2D. Suppose that we have two 2D subassemblies, each
consisting of several components, that we wish to interconnect at point A as shown
in Figure 5. The components have no meaning and are simply for illustration. We want to be
sure there are no unwanted intersections in the design, and it is clear from Figure 5 that
this assembly has no connections except at point A.
The 777 has millions of such parts, a virtual mock-up can be made from a parts and interconnection list so that designers can “fly through” the design to check for unwanted interconnections. The computer can also automatically check for such interferences so that these can be identified and redesigned before they are discovered (more dramatically and at much greater expense) during physical assembly. If there are n components we can think of an n by n matrix of pairs of potential collisions, so 3,000,000 parts would have approximately n*(n-1)/2=4.5x1012 possible intersections to be checked. Although this grows only quadratically with the number of parts (not the exponential growth we are so concerned with elsewhere) just the sheer number of parts makes brute force enumeration unattractive. Fortunately, there are quite standard ways to reduce the search.
We could begin by putting large bounding boxes around the subassemblies, as show in Figure 6. This could be used to eliminate potential intersections far away from these subassemblies (resulting in large sections of our interconnection matrix that would not need to be checked), but would not conclusively eliminate unwanted connections between the subassemblies. At this point all the pairwise components of the subassemblies could be checked, or we could refine the bounding boxes, as shown in Figure 7. At this point, we would have eliminated all but 2 components, and they could be checked to see that the only intersection was at A. The bounding boxes in this case reduced the cost from computing 24 pairwise (4x6) intersections to computing 1 pairwise component and a few bounding boxes. The bounding boxes have simple geometries so are more easily checked than the components, but need to be constructed. Clearly there is a tradeoff and one doesn’t want to use too many or too few bounding boxes.
This is an example of a general technique for searching called divide and conquer, where the problem is broken up into smaller pieces using some heuristic. It is related to branch and bound where, say, a function to be minimized is searched by successively breaking its domain into smaller pieces on which bounds of the function are computed. Suppose we want to compute the minimum distance between components that are not supposed to be connected (we want to make sure this function is bounded away from zero). A bounding box gives us upper and lower bounds on this function for the component combinations which are included in the bounding boxes. We can ignore pairs of boxes that are separated by more than the smallest upper bound we have, thus pruning the resulting tree of refined bounding boxes. This is illustrated in Figure 8 where the subassemblies are connected at point B, instead of A. The refined bounding boxes show how they can be used to focus the search for unwanted interconnections.
Note that if we introduce uncertainty in our description of the components, it can drastically increase the computation required to do pairwise checking and make the bounding box approach even more attractive. Actually, while the basics of solid modeling are well-developed, there is no standard approach to uncertainty modeling even here and many open questions. Once we introduce uncertainty in a general way, then exponential growth in evaluating all the possibilities becomes a worry. Because 3D solids inherently has limited dimensionality of contacts, it should be possible to avoid this. As we will see later, uncertainty in dynamical systems is even more challenging, and a version of the bounding box idea is quite useful in doing robustness analysis of uncertain dynamical systems as well.
It is interesting to note that the Boeing 777 used an advanced, though conventional, approach to modeling and simulation of the aerodynamics and flight. Aero modeling is a convenient example because there is a long history of successful systematic modeling, yet there remain substantial challenges. It also offers us a chance to discuss computational fluid dynamics (CFD) in a broader context that includes analytic tools, wind tunnels, and flight test. This is simply for illustration and will be very , but is illustrative of broader issues in VE.
Standard rigid body airplane models typically consist of a generic form of the model as an ordinary differential equation (ODE) with vehicle-specific parameters for mass distributions, atmospheric conditions (dynamic pressure), and aerodynamic coefficients. This rigid body model determines what motion of the vehicle will result from applied forces due to propulsion and aerodynamics. Aero coefficients are parameters that give the ratio of forces and moments generated on the vehicle to surface deflections and angular changes of the vehicle with respect to the ambient airflow. The standard quasi-steady assumption is that these aero coefficients depend only on sideslip angle and angle of attack, and not on the history of the motion of the vehicle or the complex flow around it. Therefore the aero coefficients are most compactly represented as a set of six functions, three forces and three moments, on the unit sphere (the two angles), plus additional functions for surface deflections. Obtaining these functions dominates standard aero modeling and the use of CFD.
Aero coefficients can be estimated analytically, computed using CFD, or measured in wind tunnels or flight test. The figure below shows a very rough cartoon of the error/costs associated with the various methods. Once the coefficients are obtained, they can be plugged into a dynamic model of the airplane and the resulting nonlinear differential equations can be simulated. This cartoon is misleading in many ways, but one is that the error/cost tradeoff between CFD and wind tunnel is oversimplified. The next cartoon shows the cost to find the aero coefficients at a certain number of points. Building a wind tunnel model is relatively expensive, but once it is available, the incremental time and cost to do an additional experiment is small. Research is being done to speed up both CFD and the building of wind tunnel models, thus shifting both curves to the left. One of the most revolutionary developments currently going on in this area is the improvement in rapidly generating wind tunnel models from computer models. Researchers are currently working to change the traditional turnaround time from months to hours.
This cartoon
doesn’t address the fact that CFD and wind tunnels don’t give exactly equivalent
results. To a first approximation, wind tunnel tests can give lower overall modeling error
by allowing the modeler to include additional factors, such as unsteady effects. On the
other hand, CFD can provide detailed flow field information that is difficult to obtain
experimentally and avoid experimental artifacts like wind-tunnel wall effects. Finally,
flight test give the most reliable predictions of aircraft behavior, although even here
there are errors, since not all possible operational conditions can be tested or even
necessarily anticipated. This is summarized in the first cartoon, which shows the error
versus complexity for various modeling methods. where vaguely speaking error is the
difference between predicted operational behavior and actual operational behavior, and
cost could be taken as the total dollar cost to achieve a given error with a specific
method. Note that the methods are complementary, each best for some particular
error/cost level.
They are also complementary in other ways, as the deeper nature of the errors is different as well. While the details may change with technology, the overall shape of this cartoon will not. One goal of VE is to reduce the error associated with simulation-based methods and thus reduce the need for wind tunnel and flight testing. If this is not done carefully, it is quite easy to simultaneously increase error and cost.
This discussion has taken a very superficial view of modeling and particularly of uncertainty, but has hopefully illustrated the tradeoff between error and cost that holds across both virtual and physical prototyping. One important point to note is that despite earlier euphoric visions of the role of CFD in aircraft design that suggested it would almost entirely replace wind tunnels, only a tiny fraction of the millions of aerodynamic simulations generated for a modern aircraft design are done using CFD. The remainder continue to be done with physical models in wind tunnels, and this is not expected to change in the foreseeable future. To get a slightly deeper picture of these issues, we need to examine CFD more closely.
We will briefly review the area of computational fluid dynamics relevant to the aerodynamics of aircraft, civilian or military. Fluid dynamics is a large and sophisticated technical discipline with both a long history of deep theoretical contributions and a more recent history of major technological impact, so it is not surprising that it is poorly understood by outsiders. No short account could be complete, and we will focus on the aspects of CFD that are most relevant to the broader VE enterprise.
At the speeds attained by conventional aircraft the energies imparted to the air are much too low to affect atomic or chemical processes, so there’s no need to model any features of the airflow below the molecular level. Intermolecular forces and motions are certainly significant, however, but because of the straightforward way in which molecular motions enter into the picture, the airflow can be adequately modeled by considering only scales which are large with respect to average intermolecular spacing. Rather than following a particular group of molecules, fluid dynamical models adopt a continuum view of the fluid in terms of material elements or volume elements through which the material moves. Because of the simplicity of Newtonian fluids (those for which viscosity is constant, such as air flowing about an airplane) it’s found that a fairly straightforward system of partial differential relate the dynamics of a fluid flow element to its local velocity, density, viscosity, and externally-acting forces; these are the Navier-Stokes equations, which have been known for more than a century and a half. One of the equations expresses conservation of mass and the other of momentum and the three-dimensional case has 60 partial-derivative terms.
It is widely believed that the Navier-Stokes equations adequately describe the detailed motion of air and the forces it exerts in flowing past an aircraft. More precisely, the N-S equations are thought to capture fluid phenomena well beyond the resolution of our measurement technology. Thus fluid dynamics holds a very important and extreme position in VE as an example of a domain where the resource limitation is due primarily to computation and measurement, and the basic phenomena is considered very well understood. Apparently slight variations, such as granular or chemically reacting flows change this picture dramatically, as the Navier-Stokes equations no longer apply in as straightforward a way. In any case, a major effort in fluid dynamics involves various numerical approximations to solving the Navier-Stokes or related equations. Such numerical airflow simulations are the subject of computational fluid dynamics (CFD). The obvious approach is direct numerical solution (DNS) of a discrete approximation to the Navier-Stokes equations. Unfortunately, turbulence makes this extremely difficult.
Turbulence is sometimes used informally as a catchall term for everything that’s complicated and poorly understood about fluid flow, with general characteristics that include: unsteady and irregular flows which give something of the appearance of randomness; strong vorticity; stirring and diffusion of passive conserved quantities such as heat, solutes, etc.; and dissipation of energy by momentum exchange. Turbulence has been defined mathematically for the Navier-Stokes equation as a velocity field whose spectrum has a continuous part, and similarly a signal from a measuring probe is said to be turbulent if its spectrum has a continuous part.
Under typical aircraft flight conditions at high subsonic speeds, turbulence takes the form of a nested cascade of eddies of varying scale, ranging from on the order of meters to on the order of tens of micrometers; a span of 4 or more orders of magnitude. On average, the largest eddies take energy from the free flow and, through momentum exchange, feed it down, step by step in the cascade of eddies, to the smallest eddies, where it’s dissipated as heat. However, it’s also possible for energy to feed from smaller eddies to larger over limited times or regions, and these reverse energy flows can play a significant role. Turbulence is no more random than the trajectories of our coins, but its sensitivity to initial conditions is even more dramatic, since there are so many more degrees of freedom. Turbulence was once considered one of the classic examples of chaotic dynamics, although this has not been proven. Now there is a distinction made between "weak turbulence" and "fully developed turbulence" where the former is (maybe) an example of low-dimensional chaotic dynamics, and the latter is considered as a hybrid of low-dimensional and high-dimensional chaos. It is certainly an excellent example of a highly interconnected nonlinear dynamical system.
In order fully to capture the dynamics of the airflow in DNS it is necessary to integrate numerically over a mesh fine enough to capture the smallest turbulent eddies but extensive enough to include the aircraft and a reasonable volume of air about it. This is well beyond current computational facilities although it may be possible sometime in the future, and one can make various estimates as to when that might occur. Some experts claim that this is very distant, even with the most optimistic estimates of growth in computational power. To overcome this various approximations must then be made, and these are at the heart of CFD. We will not attempt to review the multitude of approaches to CFD, but merely make a few observations. First, as was noted earlier, only a tiny fraction of the millions of aerodynamic simulations generated for a modern aircraft design are done using CFD. The remainder continues to be done with physical models in wind tunnels, and this is not expected to change in the foreseeable future. Second, CFD is used primarily to compute the static forces on objects that are fixed relative to the flow, and any dynamical vehicle motion combines these static forces with vehicle kinematics. Using CFD for computing dynamically the forces on objects which are themselves moving dynamically adds substantially to the computational complexity.
Finally, the various approaches to CFD result in widely varying computational requirements, yet there is no integrated “master” model other than the N-S equations themselves, and substantial domain-specific expertise is needed to create specific simulation models and interpret the results of simulations. Some approximations assume no viscosity and others large viscosity, some approximations focus on material elements and their motion (called Lagrangian formulations), others on volume elements through which material passes, and thus fluid velocities are the focus (called an Eulerian formulation), and still others try to track the movement of the larger scale vortical structures in the fluid. The choices are dominated by the boundary conditions, as the fluid (air) being modeled in each case is identical, and even different approximations may be made in different parts of the same flow. For example, viscosity might be modeled only near a solid boundary, while the flow far from the boundary would be assumed to be inviscid. Thus while the material itself is perfectly homogeneous, inhomogeneities arise in our necessary attempts to approximate the fluids.
What is particularly interesting for this paper is the fact that, according to Paul Rubbert, the chief aerodynamicist for Boeing, uncertainty management has become the dominant theme in practical applications like aircraft design. He claims that uncertainty management is replacing the old concept of “CFD Validation.” He argues that both CFD and wind tunnels are “notorious liars,” yet modern aerodynamic designs are increasingly sensitive to small changes and error sources. Thus better attention needs to be paid to modeling uncertainty and its consequences. CFD and wind tunnels are complementary, and the goal is to be able to reconcile the differences between their results and not to expect that they should give the same results. In this context, CFD users must be provided with the insight and understanding that allows them to manage the various sources of uncertainty that are present in their codes, and to understand how those uncertainties affect the specific aircraft behavior they are trying to predict.
In many respects, commercial aviation already is a remarkable feat in uncertainty management. We routinely get on airplanes and quite reliably arrive at our destination, and fortunately our airplanes crash much less frequently than our computers. The airplane is moving in the very complex system of the earth’s atmosphere and together with air traffic control is one enormously complex system delivering remarkably reliable transportation. At small time At large scales the atmosphere is also turbulent and chaotic, and occasional crashes due to atmospheric disturbances remind us that this is not a triviality.
Because of this turbulence in the atmosphere and near the vehicle, there is chaotic dynamics surrounding the vehicle at every scale from the microscopic to the global. Furthermore, most objects having the size and mass of a 777 and traveling at high subsonic speeds would exhibit extremely unpredictable trajectories, although eventually hitting the ground at high velocities would be a certainty. Almost any other connection of the millions of parts in a 777 would also fail to behave predictably, although the 777 itself is remarkably robust to a wide variety of component failures. Despite tremendous advances in computation and its application to CFD and CAD, no simulations are ever performed which come close to capturing all this complexity at all these scales. Yet in spite of all of this, these millions of components manage to successfully “fly in formation” such as to deliver reliable and predictable performance. Fortunately, this success in not a mystical process (that the current antiquated air traffic control works at all is fairly astonishing), but it does involve tremendous amounts of domain-specific expertise and hand-crafted solutions. We must be realistic and cautious about the way in which VE technology should interact with this process.