The present study, which was carried out in collaboration with GKN Fokker, focuses on incorporating bird strike crashworthiness requirements within a multidisciplinary optimization (MDO) framework. During the preceding three-month internship in the same company, a pivotal contribution to this project was the development of an Abaqus interface for the Multidisciplinary Modeller, MDM, created within the Center of Competence in Design department. MDM is a Python/ParaPy-based automated generator of wings, moveables and flaps, starting from a set of user-specified parameters. The generation of ready-to-run input files thus lays the foundation for the subsequent optimization process, as any changes in materials or geometry can be easily accommodated.

The core objective of the research is to minimize the weight of an aircraft wing while taking into account additional requirements related to the extent of damage caused by bird strikes. Unfortunately, such events occur more frequently than one would be comfortable with, and stringent requirements are set in place to guarantee the safety of the passengers. Among these requirements, the aircraft must be capable of landing safely after such an event, being subject to loads associated with get-home conditions.

As a consequence, two critical constraints are formulated within the optimization framework, addressing the residual strength of the damaged front spar following a bird strike, coupled with a requirement based on a maximum penetration depth. The last constraint has also been included due to the rising popularity of the electric vertical take-off and landing aircraft, which not only fly at low altitudes, thus increasing the risk of bird strike, but may also contain battery packs in the leading edge, for instance, which can pose a significant risk if damaged. To tackle the complexity of this highly-dimensional optimization challenge, a methodology based on Bayesian optimization is proposed, employing surrogate models coupled with a preliminary variable ranking procedure.

The Kriging metamodel is identified as a suitable candidate, thanks to its error prediction capabilities, which are paramount in Bayesian optimization. A variance-based dimensionality reduction method is proposed, which makes use of an initial surrogate to estimate the main and interaction effects of the variables. The quantification of the significance of a variable is expressed as its percentage contribution to the total variance, thus allowing for an intuitive selection of the most important parameters. After the screening procedure is complete, the optimization procedure is carried out in the reduced design space, which uses the constrained expected improvement as an acquisition function. The proposed methodology is then applied on a case study problem, involving a five-bay metallic wing segment subject to the constraints aforementioned, involving 19 design variables representing the thicknesses of various components.

Remarkable weight savings have been achieved, the final result being 40\% lighter than the lightest feasible design among the initial data points. A significant dimensional reduction has also been attained for the maximum depth constraint, which is expected due to the local nature of the impact. Not only did the number of variables greatly decrease from 19 to just 3, but a considerable increase in the accuracy of the corresponding metamodel has also been registered, thanks to an increase in sampling density in the reduced space. However, the variable screening procedure revealed intricate interaction effects with respect to the residual strength of the front spar, emphasizing the nuanced complexity inherent in crashworthiness considerations. Nevertheless, a moderate dimensional reduction has been achieved for this constraint as well, reducing the number of variables to 8, thus proving the efficacy of the proposed variable screening procedure.

In conclusion, the utilization of Kriging models, variable ranking procedures, and Bayesian optimization collectively contributed to the success of achieving remarkable weight savings, proving the efficiency of the proposed methodology. Moreover, it has been shown that the integration of a residual strength requirement is necessary, as many cases were uncovered where no significant penetration occurred, although the application of the considered load case, which is not from critical to an undamaged wing, resulted in high stresses to the front spar of the damaged structure. ... Read more

System architecting is one of the first stages of the engineering problem-solving process. Pivotal decisions regarding the system's overall configuration are taken in this phase. Consequently, decision support tools like system architecture optimization are needed to effectively assess the architectural design space. However, system architecture optimization problems include several features that make them challenging to tackle with traditional optimization techniques, including multiple objectives and mixed-discrete, hierarchical design spaces.

This work examines three algorithms capable of handling the mixed-discrete and multi-objective nature of system architecture optimization problems: genetic algorithms (such as NSGA-II), Bayesian optimization (BO), and the Deep Deterministic Policy Gradient (DDPG) reinforcement learning framework. These algorithms act as the engines that power three strategies capable of addressing hierarchical design spaces: \textit{global exploration}, \textit{nested optimization}, and \textit{decision chain}. While global exploration optimizes all design variables in a single loop and uses imputation on the inactive variables, the nested optimization method divides the problem into multiple hierarchical optimization loops. In contrast, the decision chain approach reframes the problem into a sequential decision-making process within an environment where an agent's actions alter design instances.

Test problems of varying complexity are used to evaluate the suitability of these algorithms and strategies. First, an airfoil optimization problem demonstrates the basic functionality of the selected algorithms with satisfactory results comparable to those found in the literature for the same problem. Next, a mixed-discrete version of the ZDT1 multi-objective problem is evaluated for different problem sizes and proportions of continuous and discrete variables. In this family of problems, the NSGA-II algorithm emerges as the most reliable and best-performing. At the same time, DDPG struggles with many variables, and Bayesian optimization runs into computational performance issues when dealing with large discrete combinatorial spaces.

Later, the architecture optimization strategies are evaluated on two versions of the Goldstein problem, a hierarchical and multi-objective test case. In the first version, which only considers eight architectures, all three strategies show competency in solving the optimization problem, but the global exploration strategy consistently shows the best performance. The decision chain strategy is discarded from further study at this stage due to relatively low performance and implementation difficulties. The second version of the Goldstein problem can be adjusted to different degrees of hierarchy and numbers of architectures. In this case, global exploration rises again as the best-performing strategy.

Finally, a real-world aileron structural optimization study at GKN Fokker shows that the implemented global exploration and nested strategies can find better designs than a random sampling of the design space. The best design for this test problem is achieved with a two-level nested strategy, combining NSGA-II in the outer loop and Bayesian optimization in the inner loop.

In conclusion, this research proposes three adaptive strategies powered by various algorithms to solve system architecture optimization problems. The findings suggest a preference for global exploration when a complete design vector can be pre-established. Otherwise, the nested optimization strategy, which can combine different algorithms' strengths and does not need a predefined design vector, emerges as the most suitable choice for more complex scenarios. ... Read more