System design in an aircraft is still a costly, manual and iterative approach. One major cost driver of changes in system installation are design efforts for creating new pipes in an earlier stage and the costs accumulated during the in service life. To reduce these costs and the time to market, an automation approach with an integrated design optimization encoded in graph-based design languages and executable in a design compiler is proposed. To generate the pipe work automatically, a set of input data (e.g., start- and end-points of a pipe with tangents and fixing positions) is given by the user. It also contains, among others, the weightings for the optimization criteria (e.g., length of the pipe resp. the weight vs. the number of bends) to influence the evaluation of the generated pipes and thereby the final solution. As an initial step in the automatic pipe generation process, a route through the installation space is searched. Subsequently, the installation space is simplified and a respective minimal distance to each obstacle which a pipe should satisfy is added. Then for each pipe an initial solution is estimated and each pipe is optimized by a simulated annealing algorithm. At last, all given requirements are automatically verified. A carried out investigation indicates a polynomial runtime behaviour of the algorithm. The capabilities of the newly developed automated piping are demonstrated on the pipe work in an Airbus A320 landing gear bay.

Pipe design in 3D is typically characterized by competing objectives, since the different design objectives, such as the reduction of length, weight, number of bends, manufacturing cost, and overall angle sum, are examples for such competing design goals, where one goal is often at the expense of the other. The origin of these competing design goals lies in the highly coupled problems of finding a permissible and collision-free pipe path in a complex 3D geometry and the physical properties of the path found. Because of the complex physics and geometry, these couplings are highly non-linear and mostly accessible via simulation only. The underlying pipe design optimization problem can thus not be solved explicitly and is tackled instead with a multi-disciplinary search procedure. Since the trade-offs between different competing evaluation objectives are often not known in advance, an automated design space exploration can be performed to generate different pipe designs, leading to well-informed design decisions by human experts. Such a design space exploration is shown and discussed using the pipework in a mounting rack in an Airbus A320 main landing gear bay. A total of 144 valid designs are generated, out of which the best in each criteria and the pareto-optimal solutions are automatically selected. Compared to the manually created Airbus A320 series solution, up to $10.4\%$ of the pipe length or up to $16.9\%$ of the bends can be saved using the same fixings and connection points, demonstrating both the feasibility and the industrial applicability of the automated toolchain.

The packing of given hydraulic equipment together with the hydraulic piping is a challenging design task. Both the hydraulic domain and the geometry domain are highly intercoupled as the packing determines the exact location of the connection points and tangents for the pipes but also defines the installation spaces for the equipment to be positioned which needs to be taken into account as an obstacle during the piping process. For the industrial case study, a mounting rack in an Airbus A320 main landing gear bay is used, where seven pieces of equipment should be packed and 22 pipes should be routed. In the first part of the study, the packing was done manually, assisted by automated routing, while the hydraulic piping was generated automatically. In the second part of the study the packing was automatized as well. For the automated packing process, a particle multi swarm optimisation was used. As objective function a pipe length minimization was implemented, which uses the Dubins Path as a pipe approximation. Constraints taken into account are the collision-free nature of the equipment and its placement on a plate inside the plates borders. The automated packing workflow was used to generate different variants of which for two a pipe work was generated exemplarily. Due to the model-based systems engineering approach, no further interaction in terms of the definition of the connection points, tangents and the installation space is necessary. This demonstrates that an automated packing and piping process in an industrial context using industrial geometries is now feasible.

Aviation is highly regulated with a strong focus on safety. If machine learning models are to be used in aviation, their correctness must be proven as part of the certification process. As the number of data points is limited in real-world applications, a new approach is needed to ensure that the behaviour between the test points is correct. Due to the complexity, it is unlikely that a method for a complete evaluation with a reasonable runtime will be found. It is demonstrated in this methodology study how, in addition to the data set, the expected behaviour of the system the model is designed for can be considered. Using domain knowledge, a specific “behaviour envelope” defines the area the model is expected to stay within. In case the model stays within the behaviour envelope, which can be mathematically evaluated, it can be ensured that the behaviour between the test points is always physically meaningful. Since the effort for the evaluation increases with the complexity, it is proposed to use symbolic regression, a method where a search procedure combines elementary functions to create a compact symbolic model. This shifts the effort more towards model creation and simplifies the subsequent validation.

In engineering, the identification of the functional relationship between a set of physical variables is a common objective. In addition to physics, an increasing number of machine learning methods are being utilised to create these models. In particular, a machine learning algorithm, generally referred to as symbolic regression (SR), generates interpretable models in the form of mathematical functions. Thus, a physical interpretation of the relationship found remains possible. While the majority of contemporary SR algorithms do not employ a systematic approach, incorporating stochastic elements, this paper proposes a novel implementation of symbolic regression. This implementation takes the form of a systematic tree search, which is deterministically spanning and searching the space of possible symbolic models. For this purpose, new mathematical models are successively generated by small modifications of an existing model, whereby the search tree grows iteratively and with it the complexity of the models. The control of the search process, and thus the selection of the model to be changed is based on a specially designed dynamic heuristic. Through the additional use of dimensional analysis, the dimensional homogeneity of the models created can be guaranteed. The efficiency of the method to arrive at interpretable models from synthetic data is illustrated by finding each of the 12 Nguyen benchmark data sets. The robustness of the approach is shown by reconstructing Breguet’s range formula from data with varying degrees of noise.