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This book contains thirty-five selected papers presented at the International Conference on Evolutionary and Deterministic Methods for Design, Optimization and Control with Applications to Industrial and Societal Problems (EUROGEN 2017). This was one of the Thematic Conferences of the European Community on Computational Methods in Applied Sciences (ECCOMAS).

Topics treated in the various chapters reflect the state of the art in theoretical and numerical methods and tools for optimization, and engineering design and societal applications. The volume focuses particularly on intelligent systems for multidisciplinary design optimization (mdo) problems based on multi-hybridized software, adjoint-based and one-shot methods, uncertainty quantification and optimization, multidisciplinary design optimization, applications of game theory to industrial optimization problems, applications in structural and civil engineering optimum design and surrogate models based optimization methods in aerodynamic design.

### Gradient Projection, Constraints and Surface Regularization Methods in Adjoint Shape Optimization

This paper deals with the treatment of various problems that are present in adjoint-based shape optimization applications, in which a parameterization of the surface is absent. A general implicit smoothing algorithm is used to reduce high-frequency noise which might be present in the gradients that are calculated using a continuous adjoint solver. The implicit smoother allows the definition of patches on the shape that need to remain fixed during shape optimization and automatically secures surface gradient continuity between constrained and deformable patches. Along with the gradient smoothing, a surface mesh regularization algorithm is presented and used to support high-quality elements and mesh uniformity during each optimization step. In the end, the capability and the effectiveness of the method are demonstrated in various industrial test cases.

Pavlos P. Alexias, Eugene de Villiers

### Adjoint Shape Optimisation Using Model Boundary Representation

Manipulating CAD geometry using primitive components rather than the originating software is typically a challenging prospect. The parameterization used to define the geometry of a model is often integral to the efficiency of the design. However, it is not always possible to access these parameters due to the closed-source, non-standardized nature of most CAD software. A sensible choice, is to use standard CAD files which have an open format, in order to read a model. Importing such a file gives access to the Boundary Representation (BRep) of the model and consequently its boundary surfaces which are usually trimmed patches. Therefore, in order to connect Adjoint optimization to the industrial design framework (CAD) in a generic manner, the BRep must be used as a means of changing a model’s shape. In this study, Geometry Morphing, a method of imposing up to C1 continuity between moving BRep patches is demonstrated and then applied to various optimization cases.

Marios Damigos, Eugene de Villiers

### CAD and Adjoint Based Multipoint Optimization of an Axial Turbine Profile

A computer-aided design (CAD) and adjoint based multipoint optimization of the LS89 high pressure axial turbine vane is presented. The aim is to reduce the entropy generation at both subsonic and transonic flow conditions by means of employing CAD and adjoint based methods during the optimization process. The performance metrics at design and off-design conditions are grouped into a single objective function using equal weights. A steady state Reynolds-Averaged density based Navier-Stokes solver and the one-equation transport Spalart-Allmaras turbulence model are used to predict the losses. The entropy generation is reduced whilst keeping the trailing edge thickness and the axial chord length as manufacturing constraints and the exit flow angle as a flow constraint, which is enforced via the penalty formulation. The resulting unconstrained optimization problem is solved by a L-BFGS-B algorithm. At every optimization iteration a new profile is constructed using B-splines and the grid is rebuilt by elliptic grid generation. The gradients used for the optimization are obtained via a novel approach in which both the CAD kernel and grid generation are differentiated using Algorithmic Differentiation techniques. The sensitivities of the objective function with respect to the grid coordinates are computed by a hand-derived adjoint solver. The off-design performance of the LS89 is significantly improved and the optimal geometry is analyzed in more detail.

Ismael Sanchez Torreguitart, Tom Verstraete, Lasse Mueller

### A Comparative Study of Two Different CAD-Based Mesh Deformation Methods for Structural Shape Optimization

Marc Schwalbach, Tom Verstraete, Jens-Dominik Müller, Nicolas Gauger

### Node-Based Adjoint Surface Optimization of U-Bend Duct for Pressure Loss Reduction

The pressure loss reduction inside the U-bends of internal cooling channels is of crucial importance to increase the performance of cooling systems of gas turbines. The optimization technique proposed in the present work is based on the continuous adjoint shape method and is implemented in the OpenFOAM open-source framework. The calculated gradients of the objective function are linked to a node-based constrained morphing routine, allowing the modification of the shape towards an optimum design with minimal pressure loss. The integration with a robust mesh morpher solver leads to successive automatic steps towards the design improvement. Design modifications take into account constraints and limitations related to the chosen design. The feasibility of the design is guaranteed by the application of a smoothing function with the aim to avoid rough external surfaces.

G. Alessi, L. Koloszar, Tom Verstraete, J. P. A. J. van Beeck

### On the Properties of Solutions of the 2D Adjoint Euler Equations

We discuss the structure of the solutions to the 2D inviscid adjoint equations on airfoils, including the behavior across shocks and sonic lines, the singularities at the forward stagnation streamline and at the trailing edges and the structure on the supersonic bubble.

Carlos Lozano

### Finite Transformation Rigid Motion Mesh Morpher

In any optimization framework, a robust and reliable mesh morpher is necessary to undertake the adaptation of the CFD mesh to the updated boundaries at each optimization cycle. Morphing has its share of challenges, namely to maintain high mesh quality (avoid distorted elements and tangles) even during extreme deformations. In this work, the Finite Transformation Rigid Motion Mesh Morpher (FT–R3M) is presented, an improved version of the Rigid Motion Mesh Morpher (Eleftheriou and Pierrot in Rigid motion mesh morpher: a novel approach for mesh deformation, 2016), that eliminates the need for sub-cycling, making it more efficient in terms of CPU time. FT–R3M, which bears some similarities to Chal et al. (ACM Trans Graph 29(4):38, 2010), is a mesh–less mesh morphing tool, since it does not require any inertial quantities, that gracefully propagates the movement of the boundaries (surface mesh) to the internal nodes of the mesh (volume mesh), by keeping the motion of its parts (referred to as stencils) as–rigid–as–possible. It is an optimization–based method, which means that the interior nodes of the computational mesh are displaced to minimize a distortion metric, namely the deformation energy. Since FT–R3M is minimizing the deformation energy between the initial and the final configuration, as opposed to R3M, in which the deformation energy is minimized from each sub-cycle to another, there is a significant gain in terms of the quality of the resulting mesh. The efficiency of the morpher proposed in this article will be demonstrated in small and medium–size cases.

Athanasios G. Liatsikouras, Guillaume Pierrot, Gabriel Fougeron, George S. Eleftheriou

### The Unsteady Continuous Adjoint Method Assisted by the Proper Generalized Decomposition Method

V. S. Papageorgiou, K. D. Samouchos, Kyriakos Giannakoglou

### A Two–Step Mesh Adaptation Tool Based on RBF with Application to Turbomachinery Optimization Loops

Adapting an unstructured CFD mesh to the modified geometry, in accordance with the updated value-set of design parameters at the end of each cycle, is a must in CFD–based shape optimization loops. Mesh adaptation is a nice alternative to remeshing procedures which might become expensive and, also, hinder the initialization of new simulations from previous results. Mesh morphing, based on Radial Basis Functions (RBF) network, has been widely used in the past to smoothly propagate boundary nodal displacements into the volume mesh while preserving its validity and quality. To precisely capture even small design changes, all surface mesh nodes must be used as interpolation nodes which, in case of large meshes for real-world application, leads to excessive computational cost and memory requirements. This paper introduces a cost reduction strategy for mesh adaptation, by proposing a new two-step RBF interpolation employing the Sparse Approximate Inverse (SPAI) preconditioner and the Fast Multipole Method (FMM). The software is demonstrated in the aerodynamic shape optimization of a turbomachinery row. The purpose of this paper is not to solve the optimization problem itself; emphasis is laid on the way the proposed method may handle large displacements and, for this reason, Evolutionary Algorithms (EA) which allow great variations in the values of the design variables were first used. Adjoint-based optimization follows; its role is to perform the refinement of the best solution obtained by the EA-based search.

Flavio Gagliardi, Konstantinos T. Tsiakas, Kyriakos Giannakoglou

### Adjoint-Based Aerodynamic Optimisation of Wing Shape Using Non-uniform Rational B-Splines

Numerical shape optimisation with adjoint CFD is applied using the NURBS-based parametrisation method with continuity constraints (NSPCC) for aerodynamically optimising three dimensional surfaces. The ONERA M6 wing is re-parametrised with NURBS surfaces including weight adjustments to represent the three dimensional wing accurately, resulting in fewer control points and smoother variation of curvature. The NSPCC CAD kernel is coupled with the in-house flow and adjoint solver STAMPS and a gradient-based optimiser to minimise the drag of the ONERA M6 wing in transonic Euler flow conditions. Optimisation results are presented for the B-Spline and NURBS parametrisations.

Xingchen Zhang, Rejish Jesudasan, Jens-Dominik Müller

### A Comparative Evaluation of Surrogate Models for Transonic Wing Shape Optimization

The paper details a comparative analysis of different models able to provide a fast response within a surrogate-based shape optimization process. Kriging, Radial Basis Function Network (RBFN) and Proper Orthogonal Decomposition in combination with RBFNs (POD+RBFN) are employed as fitness function evaluators within the framework of evolutionary algorithms (EAs). The surrogate-assisted optimization consists of initializing the surrogate with space-filling samples, improving the accuracy by adding a series of “smart” samples through specifically designed in-fill criteria and finally optimizing on the surrogate. The test case is represented by the large scale shape optimization of a transonic wing in viscous flow and in multi-design point conditions. Optimization results obtained with the surrogates by fixing the total computational budget are presented: this procedure allows to make a fair comparison between the models and their performance during the optimization process.

Emiliano Iuliano

### Study of the Influence of the Initial a Priori Training Dataset Size in the Efficiency and Convergence of Surrogate-Based Evolutionary Optimization

The development of an automatic geometry optimization tool for efficient aerodynamic shape design, supported by Computational Fluid Dynamic (CFD) methods is nowadays an attractive research field, as can be observed from the increasing number of scientific publications during the last years. Surrogate-based global optimization methods have demonstrated a huge potential to reduce the actual number of CFD runs, and therefore drastically speed-up the design process. Nevertheless, surrogates need initial high fidelity data sets to be built and to reach a proper accuracy. This work presents a study on the influence of the initial training dataset size in the proposed approach behavior. This approach is based on the use of Support Vector Machines (SVMs) as the surrogate model for estimating the objective function, in combination with an Evolutionary Algorithm (EA) and an adaptive sampling technique focused on optimization called the Intelligent Estimation Search with Sequential Learning (IES-SL). Several number of training points have been fixed to check the convergence, the accuracy and the objective function reached by the method.

Daniel González-Juarez, Esther Andrés-Pérez

### Garteur AD/AG-52: Surrogate-Based Global Optimization Methods in Preliminary Aerodynamic Design

This work presents a summary of the results obtained during the activities developed within the GARTEUR AD/AG-52 group. GARTEUR stands for “Group for Aeronautical Research and Technology in Europe” and is a multinational organization that performs high quality, collaborative, precompetitive research in the field of aeronautics to improve technological competence of the European Aerospace Industry. The aim of the AG52 group was to make an evaluation and assessment of surrogate-based global optimization methods for aerodynamic shape design of aeronautical configurations. The structure of the paper is as follows: Sect. “Introduction” will introduce the state-of-the-art in surrogate-based optimization for aerodynamic design and Sect. “Definition of Common Test Cases and Methods” will detail the test cases selected in the AG52 group. Optimization results will be then showed in Sect. “Optimization Results”, and conclusions will be provided in the last section.

Esther Andrés-Pérez, Daniel González-Juarez, Mario Martin, Emilano Iuliano, Davide Cinquegrana, Gerald Carrier, Jacques Peter, Didier Bailly, Olivier Amoignon, Petr Dvorak, David Funes, Per Weinerfelt, Leopoldo Carro, Sancho Salcedo, Yaochu Jin, John Doherty, Handing Wang

### A Response Surface Based Strategy for Accelerated Compressor Map Computation

The aim of the present work is to develop a strategy enabling fast CFD-based computation of compressor maps for aero engines. The introduced process consists of two phases. In the first phase the compressor limits due to surge and choke are identified and approximated by utilizing methods of support vector machine (SVM). These limit lines are refined within an iterative, distance-based approach. Subsequently, in the second phase the three-dimensional shape of the compressor map is approximated by a response surface method (RSM). The process is validated with an application to an industrial 4.5-stage research compressor, where very good agreement between evaluated and approximated values is obtained.

Dmitrij Ivanov, Dieter Bestle, Christian Janke

### Surrogate-Based Shape Optimization of the ERCOFTAC Centrifugal Pump Impeller

Centrifugal pumps are largely used in several fields and for different applications. Despite their wide diffusion, they are often not optimized for working at the design conditions. The aim of this paper is to investigate the potentialities offered by surrogate-based optimization techniques in centrifugal pump impeller shape optimization, to obtain a robust and fast algorithm for performance improvement. The geometry chosen for validating the proposed method is the ERCOFTAC centrifugal pump where accurate measurements and simulations are available in the literature. The three-dimensional geometry of the impeller is parametrized by means of parametric Bezier surfaces with an in-house Scilab script, which allows to export the dictionary used by the utility blockMesh to create the mesh for the CFD simulation. The surrogate-based optimization method here described maximizes the pump hydraulic efficiency, while keeping the total pressure rise prescribed to the design condition, in order to find the optimal impeller design. The whole optimization chain is designed for running in HPC environment with open-source software, i.e. OpenFOAM for CFD simulation, Dakota for the optimization and Scilab for the geometry parametrization.

Remo De Donno, Stefano Rebay, Antonio Ghidoni

### CFD Based Design Optimization of a Cabinet Nitrogen Generator

The design of mechanical enclosures is evolving to be more compact and quieter and this compromises the cooling of the internal components. Computational Fluid Dynamics (CFD) based optimization could significantly improve the cooling efficiency of the critical parts of the components to ensure their performance and reliability. This work presents the CFD surrogate based optimization of the forced cooling of two reciprocating compressors located in an enclosure from a gas generator. Due to the challenging project time constraints, the accuracy of the results was compromised to make optimization feasible. The parameters to be optimized were related to the position of the compressors and the cooling fans. The boundary conditions associated to the cooling of the critical parts were derived by experimental data. Artificial Neural Networks (ANNs) were used to construct a surrogate model of the computational model to reduce the time and resources required. The combination of the ANN model with a multi start-gradient based algorithm optimized the position of compressors and cooling fans to minimize the average temperature on the critical parts. A set of new enclosure designs were found with outstanding CFD based performance compared with the design elaborated by engineering intuition.

Bárbara Arizmendi Gutiérrez, Edmondo Minisci, Greig Chisholm

### Delaunay-Based Global Optimization in Nonconvex Domains Defined by Hidden Constraints

This paper introduces a new surrogate-based optimization algorithm to optimize a deterministic objective function with non-computable constraint functions (a.k.a. hidden constraints). Both the objective function and the feasible domain are defined within a known rectangular domain. The objective function might be nonconvex, computationally expensive, and without analytic expression. Moreover, the feasible domain boundaries are not explicitly defined, but can be determined via oracle calls (feasible or not) and learned as the algorithm proceeds. To solve this class of optimization problems, the proposed algorithm, in each iteration, approximates the feasible domain boundary by incorporating a Support Vector Machine (SVM) classifier model as an approximation for the non-computable constraint function, which characterizes the feasible domain. The uncertainty associated with this surrogate is modeled using an artificially-generated uncertainty function built on the framework of Delaunay triangulation. This work extends the Delaunay-based optimization algorithm with nonconvex constraints, dubbed $$\Delta$$ -DOGS( $$\Omega$$ ), and extends this approach to estimate the feasible domain with binary oracle calls. Similarly, this algorithm at each iteration determines a minimizer of the objective function surrogate model with the highest probability of being feasible. We evaluate the performance of the algorithm through the numerical experiments on a representative test problem.

Shahrouz Ryan Alimo, Pooriya Beyhaghi, Thomas R. Bewley

### Optimized Vehicle Dynamics Virtual Sensing Using Metaheuristic Optimization and Unscented Kalman Filter

This paper presents an Optimized Unscented Kalman Filter for vehicle dynamics virtual sensing. An automated procedure to optimize the virtual sensor parameters based on metaheuristic algorithms is presented in order to avoid the time-consuming and complex manual tuning task. Specifically, Genetic Algorithm Optimization (GA) and contrast-based Fruit Fly optimization (c-FOA) are applied to minimize the estimation error in steady-state and transient driving maneuvers. The virtual sensor is implemented in a high-fidelity vehicle dynamics simulation software (IPG-CarMaker ®) and results demonstrate the improvement of the estimation accuracy with respect to a preliminary filter tuning carried out using a systematic trial and error approach.

Manuel Acosta, Stratis Kanarachos

### Optimization of Ascent Assembly Design Based on a Combinatorial Problem Representation

The paper addresses the integration of optimization in the automated design process of ascent assemblies. The goal is to automatically search for an optimal path connecting user defined inspection points while avoiding obstacles. As a first step towards full automation of the ascent assembly design, a discrete 2D model abstraction is considered. This establishes a combinatorial optimization problem, which is tackled by the use of two distinct strategies: a greedy heuristic and a genetic algorithm variant. Applying modeling approach and algorithms to multiple test cases, partly artificial and partly based on a manufactured crane, shows that the automated ascent assembly design tasks can successfully be enhanced with optimal path planning.

Michael Hellwig, Doris Entner, Thorsten Prante, Alexandru-Ciprian Zăvoianu, Martin Schwarz, Klara Fink

### On the Optimization of 2D Path Network Layouts in Engineering Designs via Evolutionary Computation Techniques

We describe an effective optimization strategy that is capable of discovering innovative cost-optimal designs of complete ascent assembly structures. Our approach relies on a continuous 2D model abstraction, an application-inspired multi-objective formulation of the optimal design task and an efficient coevolutionary solver. The obtained results provide empirical support that our novel strategy is able to deliver competitive results for the underlying general optimization challenge: the (obstacle-avoiding) Euclidean Steiner Tree Problem.

Alexandru-Ciprian Zăvoianu, Susanne Saminger-Platz, Doris Entner, Thorsten Prante, Michael Hellwig, Martin Schwarz, Klara Fink

### Taking Advantage of 3D Printing So as to Simultaneously Reduce Weight and Mechanical Bonding Stress

3D printing is recently gaining attention, yet only few researchers address underlying design principles such as minimal thickness to shape ratio; even though they are essential to industrial applications. The authors outline an optimization and verification approach considering structural aspects such as stiffness and strength as well as producibility and structural performance. This multitude of disciplines brought forth objectives, being diametral to each other. An example is giving by simultaneous mass reduction by increasing the part’s strength performance. So as to harmonize all of those objectives to an optimal compromise, topology optimization has been used in tandem with consultations of design and structural experts. Additionally, an aerospace part, namely a 3D printed titanium insert was built and glued into an aluminium sandwich panel with carbon fiber reinforced plastic face sheets. This composite panel was then subjected to actual flight loads of the METimage satellite campaign. During all mechanical and thermal tests, cracks are captured via acoustic monitoring. Studying all test results revealed, that the approach brought forth multiple advances such as; reduced weight, increased mass-specific effective stiffness and lower mechanical bonding stresses, which increased overall structural strength.

Markus Schatz, Robert Schweikle, Christian Lausch, Michael Jentsch, Werner Konrad

### Interactive Optimization of Path Planning for a Robot Enabled by Virtual Commissioning

Optimized path planning contributes to reducing the non-productive time of material handling in fully automated manufacturing. This paper presents a case study from the machine-tool industry sector about optimization of a path planning algorithm with the goal to minimize the time a material handling gantry robot requires to follow a feedback path, i.e. feeding a just cut part again to the saw which had just cut it, in order to realize more and more complex cutting patterns. Particularities of the case study configuration led to the application of an interactive optimization approach based on the definition and manipulation of rules for smoothing of initially planned paths and the exploration of the impacts of the rules on the time the material handling robot requires for traversing these paths by means of visual examination as well as by virtual commissioning. The achieved results were deployed in plants for cutting wooden or metal panels.

Ruth Fleisch, Doris Entner, Thorsten Prante, Reinhard Pfefferkorn

### Box-Type Boom Design Using Surrogate Modeling: Introducing an Industrial Optimization Benchmark

Simulation-based optimization problems are often an inherent part in engineering design tasks. This paper introduces one such use case, the design of a box-type boom of a crane, which requires a time consuming structural analysis for validation. To overcome high runtimes for optimization approaches with numerous calls to the structural analysis tool, we here present several ways of approximating the structural analysis results using surrogate models. Results show a strong correlation between certain statics input and output parameters, and that various surrogate modeling approaches yield similar results in terms of accuracy and impact of the predictors on the output. The box-type boom use case together with the surrogate models shall serve as an industrial optimization benchmark for comparing various algorithms on this simulation-based optimization problem.

Philipp Fleck, Doris Entner, Clemens Münzer, Michael Kommenda, Thorsten Prante, Martin Schwarz, Martin Hächl, Michael Affenzeller

### Knowledge Objects Enable Mass-Individualization

Mass customization and product individualization are driving factors behind design automation, which in turn are enabled through the formalization and automation of engineering work. The goal is to offer customers optimized solutions to their needs timely and as profitable as possible. The path to achieve such a remarkable goal can be very winding and tricky for many companies, or even non-existing at the moment being. To succeed requires three essential parts: formally represented product knowledge, facilities to automatically apply the product knowledge, and optimization algorithms. This paper shows how these three parts can be supported in engineer-to-order businesses through the concept of knowledge objects. Knowledge Objects are human readable descriptions of formalized knowledge bundled with corresponding computer routines for the automation of that knowledge. One case example is given at the end of the paper to demonstrate the use of knowledge objects.

Joel Johansson, Fredrik Elgh

### Free-Form Optimization of A Shell Structure with Curvature Constraint

We present a free-form optimization method for designing the optimal shape of a shell structure with curvature constraint. Compliance is minimized under the volume and the state equation constraints. In addition, a target mean curvature of the surface is considered as the equality constraint in order to control the free-form of the shell. It is assumed that a shell is arbitrarily varied in the out-of-plane direction to the surface to create the optimal free-form. A parameter-free, or a node-based shape optimization problem is formulated in a distributed-parameter system based on the variational method. The distribution of the discrete mean curvature is calculated by the area strain obtained from the material derivative formula. The shape gradient function for this problem is theoretically derived using the Lagrange multiplier method and the adjoint variable method, and is applied to the H1 gradient method for shells. With the proposed method, the optimal free-form of a shell structure with curvature constraint can be efficiently determined. The validity and effectiveness of the method is verified through the numerical examples and the influence of the curvature constraint is demonstrated.

Masatoshi Shimoda, Kenichi Ikeya

### Application of Game Theory and Evolutionary Algorithm to the Regional Turboprop Aircraft Wing Optimization

Nash equilibrium and evolutionary algorithm are used to optimize a wing of a regional turboprop aircraft, with the aim to compare different optimization strategies in the aircraft design field. Since the aircraft design field is very complex in terms of number of involved variables and space of analysis, it is not possible to perform an optimization process accounting for all possible parameters. This leads to the need to reduce the number of the variables to the most significant ones. A multi-objective optimization approach is here performed, paying attention to the variables which mainly influence the objective functions. Results of Nash-Genetic algorithm are compared against those of both a typical Pareto front and a scalarization, showing that the proposed approach locates almost all solutions on the Pareto front, while the scalarization results are confined only in a zone of this front. The optimization elapsed time for a single optimization point is less than 32% of an entire Pareto front, but the designer must initially choose the players’ cards assignment.

Pierluigi Della Vecchia, Luca Stingo, Fabrizio Nicolosi, Agostino De Marco, Elia Daniele, Egidio D’Amato

### Industrial Application of Genetic Algorithms to Cost Reduction of a Wind Turbine Equipped with a Tuned Mass Damper

Design optimization has already become an important tool in industry. The benefits are clear, but several drawbacks are still present, being the main one the computational cost. The numerical simulation involved in the solution of each evaluation is usually costly, but time and computational resources are limited. Time is key in industry. The present communication focuses on the methodology applied to optimize the installation and design of a Tuned Mass Damper. It is a structural device installed within the tower of a wind turbine aimed to stabilize the oscillations and reduce the tensions and the fatigue loads. The paper describes the decision process to define the optimization problem, as well as the issues and solutions applied to deal with a huge computational cost.

Jordi Pons-Prats, Marti Coma, Jaume Betran, Xavier Roca, Gabriel Bugeda

### Aerodynamic Shape Optimization by Considering Geometrical Imperfections Using Polynomial Chaos Expansion and Evolutionary Algorithms

Uncertainties, in the form of either non–predictable shape imperfections (manufacturing uncertainties) or flow conditions which are not fixed (environmental uncertainties) are involved in all aerodynamic shape optimization problems. In this paper, a workflow for performing aerodynamic shape optimization under uncertainties, by taking manufacturing uncertainties into account is proposed. The uncertainty quantification (UQ) for the objective function is carried out based on the non–intrusive Polynomial Chaos Expansion (niPCE) method which relies upon the CFD software as a black–box tool. PCE is combined with an evolutionary algorithm optimization platform. CAD–free techniques are used to control the shape and simultaneously generate shape imperfections; next to this, a morphing/smoothing tool adapts the CFD mesh to any new shape. In the cases presented in this paper, all CFD evaluations are performed in the OpenFOAM environment.

Athanasios G. Liatsikouras, Varvara G. Asouti, Kyriakos Giannakoglou, Guillaume Pierrot

### Multiobjective Optimisation of Aircraft Trajectories Under Wind Uncertainty Using GPU Parallelism and Genetic Algorithms

The future Air Traffic Management (ATM) system will feature trajectory-centric procedures that give airspace users greater flexibility in trajectory planning. However, uncertainty generates major challenges for the successful implementation of the future ATM paradigm, with meteorological uncertainty representing one of the most impactful sources. In this work, we address optimized flight planning taking into account wind uncertainty, which we model with meteorological Ensemble Prediction System forecasts. We develop and implement a Parallel Probabilistic Trajectory Prediction system on a GPGPU framework in order to simulate multiple flight plans under multiple meteorological scenarios in parallel. We then use it to solve multiobjective flight planning problems with the NSGA-II genetic algorithm, which we also partially parallelize. Results prove that the combined platform has high computational performance and is able to efficiently compute tradeoffs between fuel burn, flight duration and trajectory predictability within a few seconds, therefore constituting a useful tool for pre-tactical flight planning.

Daniel González-Arribas, Manuel Sanjurjo-Rivo, Manuel Soler

### Multi-objective Optimization of A-Class Catamaran Foils Adopting a Geometric Parameterization Based on RBF Mesh Morphing

The design of sailing boats appendages requires taking in consideration a large amount of design variables and diverse sailing conditions. The operative conditions of dagger boards depend on the equilibrium of the forces and moments acting on the system. This equilibrium has to be considered when designing modern fast foiling catamarans, where the appendages accomplish both the tasks of lifting up the boat and to make possible the upwind sailing by balancing the sail side force. In this scenario, the foil performing in all conditions has to be defined as a trade-off among contrasting needs. The multi-objective optimization, combined with experienced aerodynamic design, is the most efficient strategy to face these design challenges. The development of an optimization environment has been considered in this work to design the foils for an A-Class catamaran. This study, in particular, focuses on the geometric parameterization strategy combined with a mesh morphing method based on Radial Basis Functions, and managed through the workflow integration within the optimization environment.

Marco Evangelos Biancolini, Ubaldo Cella, Alberto Clarich, Francesco Franchini

### Development of an Efficient Multifidelity Non-intrusive Uncertainty Quantification Method

Most engineering problems contain a large number of input random variables, and thus their polynomial chaos expansion (PCE) suffers from the curse of dimensionality. This issue can be tackled if the polynomial chaos representation is sparse. In the present paper a novel methodology is presented based on combination of $$\ell _1$$ -minimization and multifidelity methods. The proposed method employ the $$\ell _1$$ -minimization method to recover important coefficients of PCE using low-fidelity computations. The developed method is applied on a stochastic CFD problem and the results are presented. The transonic RAE2822 airfoil with combined operational and geometrical uncertainties is considered as a test case to examine the performance of the proposed methodology. It is shown that the new method can reproduce accurate results with much lower computational cost than the classical full Polynomial Choas (PC), and $$\ell _1$$ -minimization methods. It is observed that the present method is almost 15–20 times faster than the full PC method and 3–4 times faster than the classical $$\ell _1$$ -minimization method.

### Evolving Neural Networks to Optimize Material Usage in Blow Molded Containers

In industry, there is a growing interest to optimize the use of raw material in blow molded products. Commonly, the material in blow molded containers is optimized by dividing the container into different sections and minimizing the wall thickness of each section. The definition of discrete sections is limited by the shape of the container and can lead to suboptimal solutions. This study suggests determining the optimal thickness distribution for blow molded containers as a function of geometry. The proposed methodology relies on the use of neural networks and finite element analysis. Neural networks are stochastically evolved considering multiple objectives related to the optimization of material usage, such as cost and quality. Numerical simulations based on finite element analysis are used to evaluate the performance of the container with a thickness profile determined by feeding the coordinates of mesh elements in finite element model into the neural network. The proposed methodology was applied to the design of industrial bottle. The obtained results suggested the validity and usefulness of this methodology by revealing its ability to identify the most critical regions for the application of material.

Roman Denysiuk, Fernando M. Duarte, João P. Nunes, António Gaspar-Cunha

### Coupled Subsystem Optimization for Preliminary Core Engine Design

In this paper we present an approach for preliminary aero engine design with the overall goal to improve the core engine with regards to efficiency and emissions. This is achieved through the usage of a cascaded multi-criterion global optimization strategy, where the overall optimization is performed on the basis of decoupled black box sub-optimization of components. Such an approach has the advantage to cut down the number of design variables for each optimization problem involved and to use legacy code for components.

Simon Extra, Michael Lockan, Dieter Bestle, Peter Flassig

### Progresses in Fluid-Structure Interaction and Structural Optimization Numerical Tools Within the EU CS RIBES Project

The capability to reduce the structural weight of aircrafts, and consequently the fuel consumption, is related to the accuracy of numerical tools and to the efficiency of design methodologies available. In particular, the capability to model the interaction of the several mechanisms involved in physics phenomena represents a key point in the development of engineering design tools. Typical examples are FSI (Fluid-Structure Interaction) analyses in which the capability to properly capture the behaviour of aeroelastic phenomena is crucial. Furthermore, the enhancement of environments able to include structural shape optimizations represents a significant step forward in the development of greener aircrafts. The objectives of the EU RIBES (Radial basis functions at fluid Interface Boundaries to Envelope flow results for advanced Structural analysis) project was to reduce the uncertainness in CFD (Computational Fluid Dynamics)-CSM (Computational Structural Mechanics) aeroelastic analysis numerical methodologies, enhancing the coupling between fluid-dynamic and structural solvers, to improve the confidence on their accuracy and to progress in the development of structural optimization tools. At this aim, the project was focused on the development of an accurate load mapping procedure, on the implementation of an innovative workflow for structural shape optimization and on experimental validation of FSI (Fluid-Structure Interaction) methodologies. Radial Basis Functions (RBF) supply the mathematical foundation for the first two topics. This paper summarizes the results achieved by the project, describes the developed optimization tool and details the experimental campaign conducted to generate a database of measurements on a typical realistic aeronautical wing structure.

Marco Evangelos Biancolini, Ubaldo Cella, Corrado Groth, Andrea Chiappa, Francesco Giorgetti, Fabrizio Nicolosi