Nathalie Bartoli

Methodological enhancements in MDO process investigated in the AGILE European project

This paper presents methodological investigations performed in research activities in the field of MDO in overall aircraft design in the ongoing EU funded research project AGILE. AGILE is developing the next generation of aircraft Multidisciplinary Design and Optimization processes, which targets significant reductions in aircraft development costs and time to market, leading to cheaper and greener aircraft solutions. The paper introduces the AGILE project structure and describes the achievements of the 1st year (Design Campaign 1) leading to a reference distributed MDO system. A focus is then made on the different novel optimization techniques studied during the 2nd year, all willing to ease the optimization of complex workflows, characterized by high degree of discipline interdependencies, high number of design variables in the context of ∗Research Engineer, Information Processing and Systems Department, AIAA Member. †Post Doctoral Researcher, System Design and Performance evaluation Department ‡Research Engineer, Research and Innovation §Assistant Professor, Department of Industrial Engineering (DII), AIAA member ¶Professor, Department of Industrial Engineering (DII), AIAA member ‖Research engineer, Integrated Aircraft Design Department, AIAA member ∗∗Researcher, Propulsion Systems Aerodynamics Department

An Improved Approach for Estimating the Hyperparameters of the Kriging Model for High-Dimensional Problems through the Partial Least Squares Method

During the last years, kriging has become one of the most popular methods in computer simulation and machine learning. Kriging models have been successfully used in many engineering applications, to approximate expensive simulation models. When many input variables are used, kriging is inefficient mainly due to an exorbitant computational time required during its construction. To handle high-dimensional problems (100+), one method is recently proposed that combines kriging with the Partial Least Squares technique, the so-called KPLS model. This method has shown interesting results in terms of saving CPU time required to build model while maintaining sufficient accuracy, on both academic and industrial problems. However, KPLS has provided a poor accuracy compared to conventional kriging on multimodal functions. To handle this issue, this paper proposes adding a new step during the construction of KPLS to improve its accuracy for multimodal functions. When the exponential covariance functions are used, this step is based on simple identification between the covariance function of KPLS and kriging. The developed method is validated especially by using a multimodal academic function, known as Griewank function in the literature, and we show the gain in terms of accuracy and computer time by comparing with KPLS and kriging.

Improvement of efficient global optimization with application to aircraft wing design

For decades, numerical tool improvements enabled the optimization of complex processes occurring during the conceptual phase. Nowadays simulators can determine numerous coupled physical effects with high accuracy and allow cheap and fast virtual testing. However, high fidelity tools require long computation times (several days of computation using High Performance Computing solutions) and thus optimization based on these high fidelity tools is often done at higher computational cost (gradient based). This work aims at optimizing a complex design using costly simulation codes given a fixed computational budget. In aeronautical engineering these codes can be coupled in space (such as Fluid Structure Interaction) and/or in time (for transient analysis). The fixed budget implies the use of surrogate-based method with adaptive sampling in order to promote a trade-off between exploration and exploitation. The proposed optimization is based on a sequential enrichment approach (typically Efficient Global Optimization), using an adaptive mixture of kriging-based models. The strategy relies on an improvement of the kriging model that enables the handling of a large number of design variables whilst maintaining rapidity and accuracy. A key feature is the use of mixture of experts technique to combine local surrogate models to approximate both the objective function and the constraints. Our strategy will be introduced through mathematical methods and detailed algorithms presentation. Finally, we produce several validations on analytical test cases (supervised) and two exten- sions such as the well-known MOPTA test case from automobile industry and aircraft wing structural optimization. The experiments confirm that the proposed global optimization approach minimizes the number of black box evaluations and in this sense it is well suited for high-dimensional problems with a large number of constraints.

An adaptive optimization strategy based on mixture of experts for wing aerodynamic design optimization

In the field of aircraft design, the last few decades have focused on the iterative improve- ment of conventional tube-and-wing designs to reduce cost, noise, and emission. Never- theless, the growing expectation in terms of environment impact for the next generation of aircraft pushes for more radical changes in the design. For unconventional aircraft configurations, the need to integrate more accurate data coming from higher fidelity analysis earlier in the design process becomes more and more necessary. However, high-fidelity tools require long computation times and usually are associated with high-dimensional problems, both in terms of design variables and constraints. Therefore, these optimizations are often done at higher computational cost (gradient-based algorithms) in order to decrease the number of necessary function evaluations. In addition, the use of the adjoint method is often implemented to accurately and efficiently compute derivatives for large numbers of design variables. At the same time, new methods have been investigated to obtain opti- mized configurations at a reasonable computational cost. The work presented in this paper focuses on SEGOMOE algorithm, a solution to tackle this kind of optimization process of complex design problem through the use of an enrichment strategy approach based on mixture of experts surrogate models. Two aerodynamic shape optimization test cases, derived from cases developed by the Aerodynamic Design and Optimization Discussion Group (ADODG) are addressed: one with a single global minimum, and another one with several local minima. Both problems are nonlinearly constrained problems that involve a large number of design variables. Results are compared to gradient-based optimizers. A hybrid approach combining the advantages of both SEGOMOE and gradient-based optimization is proposed and evaluated to reduce the number of function evaluations and to ensure the convergence to the global optimum.

Towards the Industrialization of New MDO Methodologies and Tools for Aircraft Design

An overall summary of the Institute of Technology IRT Saint Exupery MDA-MDO project (Multi-Disciplinary Analysis - Multidisciplinary Design Optimization) is presented. The aim of the project is to develop efficient capabilities (methods, tools and a software platform) to enable industrial deployment of MDO methods in industry. At IRT Saint Exupery, industrial and academic partners collaborate in a single place to the development of MDO methodologies; the advantage provided by this mixed organization is to directly benefit from both advanced methods at the cutting edge of research and deep knowledge of industrial needs and constraints. This paper presents the three main goals of the project: the elaboration of innovative MDO methodologies and formulations (also referred to as architectures in the literature 1) adapted to the resolution of industrial aircraft optimization design problems, the development of a MDO platform featuring scalable MDO capabilities for transfer to industry and the achievement of a simulation-based optimization of an aircraft engine pylon with industrial Computational Fluid Dynamics (CFD) and Computational Structural Mechanics (CSM) tools.

Exploration and Sizing of a Large Passenger Aircraft with Distributed Ducted Electric Fans

In order to reduce the CO2 emissions, a disruptive concept in aircraft propulsion has to be considered. As studied in the past years hybrid distributed electric propulsion is a promising option. In this work the feasibility of a new concept aircraft, using this technology, has been studied. Two different energy sources have been used: fuel based engines and batteries. The latters have been chosen because of their exibility during operations and their promising improvements over next years. The technological horizon considered in this study is the 2035: thus some critical hypotheses have been made for electrical components, airframe and propulsion. Due to the uncertainty associated to these data, sensivity analyses have been performed in order to assess the impact of technologies variations. To evaluate the advantages of the proposed concept, a comparison with a conventional aircraft(EIS 2035), based on evolutions of todays technology (airframe, propulsion, aerodynamics)has been made.

A clustered and surrogate-based MDA use case for MDO scenarios in AGILE project

In this paper methodological investigations regarding an innovative Multidisciplinary Design and Optimization (MDO) approach for conceptual aircraft design are presented. These research activities are part of the ongoing EU-funded research project AGILE. The next generation of aircraft MDO processes is developed in AGILE, which targets significant reductions in aircraft development cost and time to market, leading to cheaper and greener aircraft solutions. The paper introduces the AGILE project structure and recalls the achievements of the first year of activities where a reference distributed MDO system has been formulated, deployed and applied to the design and optimization of a reference conventional aircraft configuration. Then, investigations conducted in the second year are presented, all aiming at making the complex optimization workflows easier to handle, characterized by a high degree of discipline interdependencies, multi-level processes and multi-partner collaborative engineering activities. The paper focuses on an innovative approach in which knowledge-based engineering and collaborative engineering techniques are used to handle a complex aircraft design workflow. Surrogate models replacing clusters of analysis disciplines have been developed and applied to make workflow execution more efficient. The paper details the different steps of the developed approach to set up and operate this test case, involving a team of aircraft design and surrogate modelling specialists, and taking advantage of the AGILE MDO framework. To validate the approach, different executable workflows were generated automatically and used to efficiently compare different MDO formulations. The use of surrogate models for clusters of design competences have been proved to be efficient approach not only to decrease the computational time but also to benchmark different MDO formulations on a complex optimization problem.

Noise Filtering and Uncertainty Quantification in Surrogate based Optimization

Dense layers of solid particles surrounding a high energy explosive generate jet-like structures at later times after detonation. Conjectures as to the cause of these jet structures include inhomogeneities in the initial distribution of particles. We characterize this variation as particle volume fraction (PVF), defined as volume of particles divided by the volume of gas and particles in a computational cell. We explore what trimodal sinusoidal initial PVF variation would lead to the observed jet formation. This is done by looking for mode shape parameters that amplify most rapidly via optimization. Because the initial perturbations are small they take time to develop, which places a large computational burden on the simulation. We therefore use large initial imperfections that develop into finger-like structures more rapidly. To reduce further the computational cost of the optimization we build a surrogate model. An initial hurdle was to select an objective function that would measure the growth of the initial perturbations. After substantial analysis and numerical experimentation, we settled on the departure from cylindrical symmetry in the particle distribution. The variables considered are the parameters of a trimodal sinusoidal perturbation (amplitudes, wavelengths, and phases). We observed substantial noise in the objective function due to a combination of randomness in the initial position of the particles and the use of Cartesian coordinates for a cylindrically symmetric problem. Since a noisy function is more difficult to optimize, the noise was reduced by a Fourier filter we have developed. We present a novel technique to measure uncertainties using the problem dihedral symmetries. Although it can be applied to the general case in nine variables (3 amplitudes, 3 wave-numbers and 3 phases) we present a simplified problem in three variables. If the amplitude for each of the three modes is kept the same and there is no phase shift, the order of the wave-numbers does not matter, i.e. the case with wave-numbers (k1, k2, k3) should have the same output than its permutations (k1, k3, k2), (k2, k1, k3), (k2, k3, k1), (k3, k1, k2), (k3, k2, k1). Therefore, for each point simulated, we have five extra validation points that we call permutation points, ready to be used to compute uncertainty. We found range-normalized errors up to 33%.

Improvement of the Aircraft Design process for Air Traffic Management evaluations

In the field of Aircraft Design, new transport concepts rely heavily on aero-propulsive effects with the objective of providing step changes in terms of energy consumption. Given the strong dependency of the level of lift with respect to engine settings, there is an added value for the designers to complete full simulations of the operational mission to verify the viability of the selected architecture. Regarding Air Traffic Management, the need for more accurate trajectories as well as solutions to characterize new aircraft in the air space has been identified. Taking the opportunity of these shared requirements, the authors present in this paper the coupling between a conceptual design sizing tool and an ATM simulator. The objective is to pave the way for future optimizations of the global system where aircraft would be designed taking into account real flight routes defined by ATM constraints. To validate the simulation model generated by the sizing code, resulting climb trajectories as well as initial cruise phases are compared with real flight traces recorded with an ADS-B antenna.

Similarity maximization of a scaled aeroelastic flight demonstrator via multidisciplinary optimization

The developments presented in this paper take place in the context of a broader series of works carried out at ONERA and ISAE-SUPAERO on multidisciplinary design optimization applied to a scaled flight demonstrator. The aim of this work is to develop an optimization process capable of sizing a scaled flight demonstrator in order to reproduce several behaviors en- countered on its corresponding full size aircraft. Unlike the classical optimization problems found in aeronautics, whose objective functions are performance-related (e.g. mass and drag minimization), we aim to maximize the similarity between the scaled model and the full size aircraft. In the aforementioned context, the first part of this paper corresponds to the static aeroelastic similarity problem. However, the approach described herein is general enough to treat other optimization problems, including performance-related ones. The second part of this work deals with the dynamic aspects of the aeroelastic similar- ity. A benchmark case is presented where the structural properties of a given geometry are optimized in order to match the reference modal parameters (i.e., mode shapes and frequencies) of the GARTEUR SM-AG19 model.