# Searching the Space of Topologies

One of the key thrusts of this book is the application of computational engineering tools to the systematic search for the optimal solution to the problem of designing a fixed-wing unmanned aircraft in response to a design brief. A neat storyline would demand, at this point, an immediate start along these lines - specifically, an algorithm that converts the design brief into a topology, ideally without any intervention from the engineer who is there merely to oversee the process, but allows a suite of physics-based analysis codes and optimizers to do the actual decision making. For example, entering a service ceiling of 30 km and an endurance of 24 h would result in an automated computational search yielding, eventually, the topology of the Helios aircraft shown at the bottom of Figure 10.2 (or whatever the optimal topology may be).

Alas, we are unable to offer such an algorithm here. In fact, the aerospace industry is divided even on the question of whether such computational machinery will ever exist. It is not inconceivable that a layout like that of the Scaled Composites Proteus (top of Figure 10.2) will be generated by an algorithm in response to a design brief - say, carry a one ton payload to a 15 km service ceiling - but for the algorithm to be truly a step forward from the status quo, the expectation would be that it would also supply a guarantee that the Proteus-like layout will be the *best* for an aircraft designed to carry a one ton payload to a 15 km service ceiling.^{[1]} Of course, this is an extremely hard multidisciplinary and multiobjective problem and it would be unreasonable to hold the design tool to such a high standard; but then *what standard should we hold it to?* What should the objectives be? What should the stopping criterion of the search be?

The structural engineering community has made significant strides toward solving a small subproblem of the vast optimal topology question, namely the single-discipline, single-objective question of what is the topology of the minimum mass part designed to withstand a given set of loading conditions. Consider the simple problem of holding a point load at the end of a cantilever fixed at its root with two bolts. What network of nonlinear members would carry this load in the most mass-efficient manner? How should these members be connected to each other? As it happens, this problem even has an analytically verifiable global optimum, which is shown in Figure 10.3.

This is an elegant solution, but the problem is a very simple one, even within the one load case, one discipline, and one objective category. More complicated problems are solvable via numerical methods (though generally not quite as neatly as in this example), typically based on the iterative removal of underutilized material. Linear elastic structural design also receives an enormous boost in the shape of a theorem which states that a framework whose members all carry stresses equal to the “allowable stress” dictated by the material will be no heavier than any other framework occupying the same region of space and subject to the same boundary conditions. This is phenomenally useful, because if, by whatever means, we find the optimal

**Figure 10.2 **Four semi-randomly chosen points in an immense space of unmanned aircraft topologies: (starting at the top) the Scaled Composites Proteus, the NASA Prandtl-D research aircraft, the AeroVi- ronment RQ-11 Raven, and the NASA Helios (images courtesy of NASA and the USAF).

**Figure 10.3 **Minimum mass cantilever designed to carry a point load.

solution to the topology problem, *we will know that we have the optimum* - the familiar stress plot will all be a uniform color.^{[2]} In other words, the route to the optimum may not be obvious, but the stopping criterion, at least, is (provided that the picture is not complicated by multiple load cases, buckling, etc.).

Stepping back to regard the big picture of the topology of the whole airplane, we have none of these luxuries: no analytical or numerical methods guiding us toward optima (we cannot start, say, with hundreds of wings and remove the unwanted ones iteratively), no neat theorem telling us that we have arrived at the solution, a plethora of disciplines and constraints shrouded in complex physics, mathematics, and economics, and, most pressingly, an objective function whose identity is not even clear in most cases (is it life-cycle cost? is it some performance metric?).

Looking to the future, all is not lost in terms of automating the concept design process. The use of genetic programming (GP) for *automated invention* has been advocated by Koza [16] and others since the 1980s and has seen some success in, for example, the automated discovery of electronic circuits (relatively simple physics compared to the flight of an aircraft!). In terms of applying this sort of evolutionary technology to aircraft concept design, there are two challenges:

- • The physics-based analysis capability behind the computation of the GP fitness function has to be extremely fast (analytical models and look-up table methods are sensible candidates) - commensurate with the large number of putative designs offered by a typical evolutionary process.
- • A parametric model has to be built that balances topological flexibility against the size of the design space and offers an encoding that is well suited to GP implementation.

As for the latter challenge, there is an obvious candidate that lends itself to GP: tree structures. It is also relatively easy to imagine a tree structure describing the connectivity of the components of a UAV airframe. The definitions of the terminals of the tree might take advantage of some simple functional classification of the components that make up aircraft, for example, enclosure type components (whose function is to enclose a payload, fuel or some onboard system), lifting surfaces (including everything from the main wings to winglets, fins, etc.), and propulsion system components (see Ref. [17] for a proposed parameterization along these lines).

While the technology readiness level of such ideas remains largely between “speculation” and “trying a few things,” we need to consider an alternative strategy that, while informed by engineering analysis, is steered directly by the engineer.

- [1] Of course, these are just two headline numbers from the myriad targets and criteria the “real” aircraft would bedesigned against - see Section 10.1.3.
- [2] Of course, in “real” design practice, life is never quite as kind as this and the picture will always be a bit messierthan that, but fundamentally the more uniform the stress field, the closer we are to the optimum.