This study introduces SEGOMOE, a Bayesian optimization tool for optimizing complex, computationally expensive systems, especially in aeronautics. It efficiently handles mixed design variables (continuous, discrete, categorical, hierarchical) using adaptive Gaussian process models. SEGOMOE combines expert models to address nonlinearities in objectives and constraints, leveraging the open-source Surrogate Modeling Toolbox (SMT). The tool supports multi-fidelity data and solves both single- and multi-objective problems, including hidden constraints and high-dimensional decomposition. Validated through benchmarks and real-world aeronautical applications, SEGOMOE proves to be robust and versatile for tackling multidisciplinary challenges.

Vertical takeoff and landing unmanned aerial vehicles are attractive for missions where flight dexterity and long ranges are needed. However, designing such a kind of vehicle is troublesome, considering its broad flight envelope and controllability challenges. This paper focuses on the problem of simultaneously optimizing their design, trajectory, and control laws. It starts with the description of the flight mechanics model, the two-fidelity aerodynamic method used for integrated aeropropulsive analysis, and the 3D modeling strategy that allows for weight and inertia prediction using the Engineering Sketch Pad. A 2D trajectory optimization problem that accounts for a representative mission with hover, transition hover-cruise, cruise, climb, and transition cruise-hover is presented and solved for fixed and varying vehicle designs, with the latter case generating better results. We perform a closed-loop analysis of the optimal open-loop trajectory under steady wind conditions and find that, in this case, the solution lacks robustness to the applied disturbance. Different strategies to integrate the closed-loop analysis and control law design optimization in the vehicle-trajectory problem are presented and discussed. The simultaneously optimized vehicle-trajectory-control solution is capable of rejecting the steady wind, flying within a defined flight corridor, at the cost of being 12.50% less energy efficient.

The aviation industry continually strives to improve the safety, efficiency, and reliability of aircraft. With an increasing focus on novel aircraft configurations to reduce the environmental impact of aviation, aircraft have become even more complex than before. Model Based Systems Engineering (MBSE), Model Based Safety Assessment (MBSA), and Multidisciplinary Design Analysis and Optimization (MDAO) have thereby gained popularity over the document-centric approach in the past decade. The common integration strategy - extending the model within a single MBSE framework - inherently reduces the use of unique capabilities of specialized MBSA and MDAO platforms. This position paper proposes an alternative methodology utilizing model transformation techniques to develop a robust link between these domains. This is achieved via a custom script extracting and transforming relevant information from an MBSE model file into file formats required by MBSA/MDAO tools. The primary contribution is maintaining consistency through a novel iterative design process formalizing the model transformation. This approach ensures the preservation of extensive capabilities offered by each domain-specific tool. Formalism is supported by implementing QVTo mapping rules and strengthening the verification with OCL constraints and Python codes developed to ensure that bidirectional transformations occur without information loss or distortion. This systematic integration streamlines the design process by enabling parallel safety assessment from an early design phase and facilitating a comprehensive exploration of the design space, thereby fostering informed decision-making. The technical feasibility of this methodology is demonstrated through its application on a UAVcase study, establishing a foundation for future development and real aerospace applications.

Bayesian optimization is an advanced tool to perform ecient global optimization It consists on enriching iteratively surrogate Kriging models of the objective and the constraints both supposed to be computationally expensive of the targeted optimization problem Nowadays efficient extensions of Bayesian optimization to solve expensive multiobjective problems are of high interest The proposed method in this paper extends the super efficient global optimization with mixture of experts SEGOMOE to solve constrained multiobjective problems To cope with the illposedness of the multiobjective inll criteria different enrichment procedures using regularization techniques are proposed The merit of the proposed approaches are shown on known multiobjective benchmark problems with and without constraints The proposed methods are then used to solve a biobjective application related to conceptual aircraft design with ve unknown design variables and three nonlinear inequality constraints The preliminary results show a reduction of the total cost in terms of function evaluations by a factor of 20 compared to the evolutionary algorithm NSGA-II.

In the last decades, several studies show how the concurrent evaluation of manufacturing and supply chain in the early design phase brings significant advantages to industries. In this frame, a value-driven methodology has been developed and applied in the aeronautical context to identify the best solution when considering design, manufacturing, and supply chain criteria at the same time. This study aims at including optimization algorithms in the methodology to face a new challenge: the identification of solutions simultaneously optimizing manufacturing, design, and supply chain variables. To achieve this objective, collaborative optimization problems are presented in this research activity in three multidisciplinary design and optimization (MDO) cases, which integrate domains first in pairs and then together. Shortly, MDO case I identifies a Pareto front of optimal supply chain combinations producing aircraft components among millions of possibilities after several hours of execution; MDO case II shows the optimal aircraft configuration made by considering hundreds of combinations of materials and processes in less than one hour; MDO case III reaches the Pareto front in a half-day considering millions of choices of materials, processes, and enterprises.

For developing innovative systems architectures, modeling and optimization techniques have been central to frame the architecting process and define the optimization and modeling problems. In this context, for system-of-systems the use of efficient dedicated approaches (often physics-based simulations) is highly recommended to reduce the computational complexity of the targeted applications. However, exploring novel architectures using such dedicated approaches might pose challenges for optimization algorithms, including increased evaluation costs and potential failures. To address these challenges, surrogate-based optimization algorithms, such as Bayesian optimization utilizing Gaussian process models have emerged.

Vertical takeoff and landing (VTOL) vehicles are among the most versatile UAVs, appropriate for various missions. Given that there are still open challenges regarding the VTOL design, this paper presents the full development and test cycle of a tail-sitter. IMAV 2022 competition rules were used to define the mission. A multidisciplinary design and optimization strategy was defined with the goal of maximizing competition score considering design, manufacturing, and competition constraints. The resulting vehicle was designed to fly at 18m/s while carrying 200 g of payload with a total weight of approximately 720 g. It flew for roughly 13 min at IMAV2022, helping its team to achieve 1st place at the " Package delivery challenge". Further flight tests revealed the ultimate endurance performance as 18min.

Choosing the right system architecture for the problem at hand is challenging due to the large design space and high uncertainty in the early stage of the design process. Formulating the architecting process as an optimization problem may mitigate some of these challenges. This work investigates strategies for solving system architecture optimization (SAO) problems: expensive, black-box, hierarchical, mixed-discrete, constrained, multi-objective problems that may be subject to hidden constraints. Imputation ratio, correction ratio, correction fraction, and max rate diversity metrics are defined for characterizing hierarchical design spaces. This work considers two classes of optimization algorithms for SAO: multi-objective evolutionary algorithms such as NSGA-II, and Bayesian optimization (BO) algorithms. A new Gaussian process kernel is presented that enables modeling hierarchical categorical variables, extending previous work on modeling continuous and integer hierarchical variables. Next, a hierarchical sampling algorithm that uses design space hierarchy to group design vectors by active design variables is developed. Then, it is demonstrated that integrating more hierarchy information in the optimization algorithms yields better optimization results for BO algorithms. Several realistic single-objective and multi-objective test problems are used for investigations. Finally, the BO algorithm is applied to a jet engine architecture optimization problem. This work shows that the developed BO algorithm can effectively solve the problem with one order of magnitude less function evaluations than NSGA-II. The algorithms and problems used in this work are implemented in the open-source Python library SBArchOpt.

The Surrogate Modeling Toolbox (SMT) is an open-source Python package that offers a collection of surrogate modeling methods, sampling techniques, and a set of sample problems. This paper presents SMT 2.0, a major new release of SMT that introduces significant upgrades and new features to the toolbox. This release adds the capability to handle mixed-variable surrogate models and hierarchical variables. These types of variables are becoming increasingly important in several surrogate modeling applications. SMT 2.0 also improves SMT by extending sampling methods, adding new surrogate models, and computing variance and kernel derivatives for Kriging. This release also includes new functions to handle noisy and use multi-fidelity data. To the best of our knowledge, SMT 2.0 is the first open-source surrogate library to propose surrogate models for hierarchical and mixed inputs. This open-source software is distributed under the New BSD license.2

System Architecture Optimization (SAO) can support the design of novel architectures by formulating the architecting process as an optimization problem.The exploration of novel architectures requires physics-based simulation due to a lack of prior experience to start from, which introduces two specific challenges for optimization algorithms: evaluations become more expensive (in time) and evaluations might fail.The former challenge is addressed by Surrogate-Based Optimization (SBO) algorithms, in particular Bayesian Optimization (BO) using Gaussian Process (GP) models.An overview is provided of how BO can deal with challenges specific to architecture optimization, such as design variable hierarchy and multiple objectives: specific measures include ensemble infills and a hierarchical sampling algorithm.Evaluations might fail due to non-convergence of underlying solvers or infeasible geometry in certain areas of the design space.Such failed evaluations, also known as hidden constraints, pose a particular challenge to SBO/BO, as the surrogate model cannot be trained on empty results.This work investigates various strategies for satisfying hidden constraints in BO algorithms.Three high-level strategies are identified: rejection of failed points from the training set, replacing failed points based on viable (non-failed) points, and predicting the failure region.Through investigations on a set of test problems including a jet engine architecture optimization problem, it is shown that best performance is achieved with a mixed-discrete GP to predict the Probability of Viability (PoV), and by ensuring selected infill points satisfy some minimum PoV threshold.This strategy is demonstrated by solving a jet engine architecture problem that features at 50% failure rate and could not previously be solved by a BO algorithm.The developed BO algorithm and used test problems are available in the open-source Python library SBArchOpt.

Recently, there has been a growing interest in mixed-categorical metamodels based on Gaussian Process (GP) for Bayesian optimization. In this context, different approaches can be used to build the mixed-categorical GP. Many of these approaches involve a high number of hyperparameters; in fact, the more general and precise the strategy used to build the GP, the greater the number of hyperparameters to estimate. This paper introduces an innovative dimension reduction algorithm that relies on partial least squares regression to reduce the number of hyperparameters used to build a mixed-variable GP. Our goal is to generalize classical dimension reduction techniques commonly used within GP (for continuous inputs) to handle mixed-categorical inputs. The good potential of the proposed method is demonstrated in both structural and multidisciplinary application contexts. The targeted applications include the analysis of a cantilever beam as well as the optimization of a green aircraft, resulting in a significant 439-kilogram reduction in fuel consumption during a single mission.

In aerodynamics, characterizing the aerodynamic behavior of aircraft typically requires a large number of observation data points. Real experiments can generate thousands of data points with suitable accuracy, but they are time-consuming and resource-intensive. Consequently, conducting real experiments at new input configurations might be impractical. To address this challenge, data-driven surrogate models have emerged as a cost-effective and time-efficient alternative. They provide simplified mathematical representations that approximate the output of interest. Models based on Gaussian Processes (GPs) have gained popularity in aerodynamics due to their ability to provide accurate predictions and quantify uncertainty while maintaining tractable execution times. To handle large datasets, sparse approximations of GPs have been further investigated to reduce the computational complexity of exact inference. In this paper, we revisit and adapt two classic sparse methods for GPs to address the specific requirements frequently encountered in aerodynamic applications. We compare different strategies for choosing the inducing inputs, which significantly impact the complexity reduction. We formally integrate our implementations into the open-source Python toolbox SMT, enabling the use of sparse methods across the GP regression pipeline. We demonstrate the performance of our Sparse GP (SGP) developments in a comprehensive 1D analytic example as well as in a real wind tunnel application with thousands of training data points.

Recently, there has been a growing interest for mixed-categorical meta-models based on Gaussian process (GP) surrogates. In this setting, several existing approaches use different strategies either by using continuous kernels ( e.g. , continuous relaxation and Gower distance based GP) or by using a direct estimation of the correlation matrix. In this paper, we present a kernel-based approach that extends continuous exponential kernels to handle mixed-categorical variables. The proposed kernel leads to a new GP surrogate that generalizes both the continuous relaxation and the Gower distance based GP models. We demonstrate, on both analytical and engineering problems, that our proposed GP model gives a higher likelihood and a smaller residual error than the other kernel-based state-of-the-art models. Our method is available in the open-source software SMT.

This work aims at developing new methodologies to optimize computational costly complex systems (e.g., aeronautical engineering systems). The proposed surrogate-based method (often called Bayesian optimization) uses adaptive sampling to promote a trade-off between exploration and exploitation. Our in-house implementation, called SEGOMOE, handles a high number of design variables (continuous, discrete or categorical) and nonlinearities by combining mixtures of experts for the objective and/or the constraints. Additionally, the method handles multi-objective optimization settings, as it allows the construction of accurate Pareto fronts with a minimal number of function evaluations. Different infill criteria have been implemented to handle multiple objectives with or without constraints. The effectiveness of the proposed method was tested on practical aeronautical applications within the context of the European Project AGILE 4.0 and demonstrated favorable results. A first example concerns a retrofitting problem where a comparison between two optimizers have been made. A second example introduces hierarchical variables to deal with architecture system in order to design an aircraft family. The third example increases drastically the number of categorical variables as it combines aircraft design, supply chain and manufacturing process. In this article, we show, on three different realistic problems, various aspects of our optimization codes thanks to the diversity of the treated aircraft problems.

Black-box optimization methods like Bayesian optimization are often employed in cases where the underlying objective functions and their gradient are complex, expensive to evaluate, or unavailable in closed form, making it difficult or impossible to use traditional optimization techniques. Fixed-wing drone design problems often face this kind of situations. Moreover in the literature multi-fidelity strategies allow to consistently reduce the optimization cost for mono-objective problems. The purpose of this paper is to propose a multi-fidelity Bayesian optimization method that suits to multi-objective problem solving. In this approach, low-fidelity and high-fidelity objective functions are used to build co-Kriging surrogate models which are then optimized using a Bayesian framework. By combining multiple fidelity levels and objectives, this approach efficiently explores the solution space and identifies the set of Pareto-optimal solutions. First, four analytical problems were solved to assess the methodology. The approach was then used to solve a more realistic problem involving the design of a fixed-wing drone for a specific mission. Compared to the mono-fidelity strategy, the multi-fidelity one significantly improved optimization performance. On the drone test case, using a fixed budget, it allows to divide the inverted generational distance metric by 6.87 on average.

View Video Presentation: https://doi.org/10.2514/6.2023-2366.vid Nowadays, drones can be developed for a wide range of use cases, from infrastructure monitoring to sea rescue, urban mobility or military purposes. Which drone design is best suited for a specific mission? To answer this question, we need to solve a constrained optimization problem based on a multi-disciplinary design model that takes the mission into account. The model generally being a computationally expensive numerical model whose gradients are not available all the time encourages us to consider a Bayesian optimization approach. Such strategy is well known to achieve a trade-off between exploitation and exploration in order to find interesting minimal area with a reduced number of function evaluations. A multi-fidelity approach can improve even more the computational efficiency of the Bayesian optimization strategy. In this work, we aim at designing a fixed-wing drone (fully electric) for long range surveillance mission. Two fidelity level electric drone models are developed. For a given mission requirement, the final battery state of charge is optimized with respect to drone design variables. Optimizations are performed on several missions using both a mono and a multi-fidelity Bayesian optimization strategy. The interest of using a multi-fidelity method for overall drone design has been assessed. The multi-fidelity super-efficient global optimization algorithm (MFSEGO) appeared to need less budget to reach convergence than the mono-fidelity algorithm and to be more robust to the initial design of experiments.

In the last decades, some studies have highlighted that the integration of the product design and supply chain management leads to an increase of the profitability and efficiency of companies. However, considering manufacturing, supply chain and overall aircraft design variables in the early design phase increases the size of the solutions tradespace and thus the complexity in performing the decision‐making process. This paper, follow‐up of previous research activities addressed within the European project AGILE4.0, demonstrates how to leverage the value‐model theory to simplify the decision‐process when multiple criteria are accounted in the design phase.

In the last decades, several studies demonstrate how the integration of manufacturing and supply chain in the early design phase brings significant advantages to industries. Within the European Project (AGILE 4.0, 2022), a value‐driven methodology concurrently coupling design, manufacturing and supply chain has been developed. This study aims at addressing a new challenge: the identification of non‐dominated solutions simultaneously accounting for manufacturing, design and supply chain variables. For this purpose, an optimization design campaign has been addressed in this research activity and the main results are‐here presented.