State-of-the-art in aerodynamic shape optimisation methods

Aerodynamic optimisation has become an indispensable component for any aerodynamic design over the past 60 years, with applications to aircraft, cars, trains, bridges, wind turbines, internal pipe flows, and cavities, among others, and is thus relevant in many facets of technology. With advancements in computational power, automated design optimisation procedures have become more competent, however, there is an ambiguity and bias throughout the literature with regards to relative performance of optimisation architectures and employed algorithms. This paper provides a well-balanced critical review of the dominant optimisation approaches that have been integrated with aerodynamic theory for the purpose of shape optimisation. A total of 229 papers, published in more than 120 journals and conference proceedings, have been classified into 6 different optimisation algorithm approaches. The material cited includes some of the most well-established authors and publications in the field of aerodynamic optimisation. This paper aims to eliminate bias toward certain algorithms by analysing the limitations, drawbacks, and the benefits of the most utilised optimisation approaches. This review provides comprehensive but straightforward insight for non-specialists and reference detailing the current state for specialist practitioners

New sampling strategies when searching for robust solutions

Many real-world optimisation problems involve un- certainties, and in such situations it is often desirable to identify robust solutions that perform well over the possible future scenarios. In this paper, we focus on input uncertainty, such as in manufacturing, where the actual manufactured product may differ from the specified design but should still function well. Estimating a solution’s expected fitness in such a case is challenging, especially if the fitness function is expensive to evaluate, and its analytic form is unknown. One option is to average over a number of scenarios, but this is computationally expensive. The archive sample approximation method reduces the required number of fitness evaluations by re-using previous evaluations stored in an archive. The main challenge in the application of this method lies in determining the locations of additional samples drawn in each generation to enrich the information in the archive and reduce the estimation error. In this paper, we use the Wasserstein distance metric to approximate the possible benefit of a potential sample location on the estimation error, and propose new sampling strategies based on this metric. Contrary to previous studies, we consider a sample’s contribution for the entire population, rather than inspecting each individual separately. This also allows us to dynamically adjust the number of samples to be collected in each generation. An empirical comparison with several previously proposed archive-based sample approximation methods demonstrates the superiority of our approaches

Multidisciplinary optimisation of an Unmanned Aerial Vehicle with a fuel cell powered energy system

ALF/ENGAER 139425-J Bernardo Miguel Teixeira Alves. Examination Committee: Chairperson: COR/ENGAER Luís António Monteiro Pessanha; Supervisors: Prof. André Calado Marta, MAJ/ENGAER Luís Filipe da Silva Félix; Member of the Committee: Prof. Pedro Vieira GamboaPara explorar a utilização de células de combustível a hidrogénio como alternativa viável aos combustíveis nocivos em veículos aéreos não-tripulados, um conceito de UAV de classe I foi desenvolvido no Centro de Investigação da Força Aérea (CIAFA). Este trabalho foca-se nos estudos trade-off realizados durante a sua conceção e na subsequente otimização. Primeiro, uma abordagem de otimização multi-objetivo foi utilizada com o auxílio do algoritmo genético NSGA-II para balancear dois objetivos em conflito: peso reduzido; e elevada autonomia. Conclui-se que é possível voar mais de três horas com um peso máximo à descolagem de 21,6 kg, uma célula de hidrogénio de 800 W e 148 g de hidrogénio. Uma configuração mais pesada com maior potência nominal e mais combustível foi descartada devido a um constragimento na envergadura. Posteriormente, com um conceito que satisfaz os requisitos impostos, uma abordagem multi-disciplinar (MDO) foi utilizada para maximizar a autonomia. O software utilizado foi o OpenAeroStruct, método dos elementos finitos (FEM) e o método da malha de vórtices (VLM) para modelar superfícies sustentadoras. Inicialmente, uma condição de cruzeiro e de carga foram utilizadas com torção geométrica da asa como variável de projeto. Posteriormente, maior complexidade foi introduzida atrav´es da utilização de afilamento, corda e envergadura. Finalmente, uma terceira condição de voo foi introduzida com o intuito de garantir o requisito de perda. Com a utilização de MDO foi possível aumentar a autonomia em 21% satisfazendo todos os requisitos. Este trabalho marca um passo importante no desenvolvimento de um futuro protótipo no Centro de Investigação.To explore the use of hydrogen fuel cells as a feasible alternative to pollutant fuels on Unmanned Aerial Vehicles (UAVs), a class I concept was designed at the Portuguese Air Force Research Centre. This work focuses on the trade-off studies performed during its design and on the optimisation that followed. First, a multi-objective optimisation approach was used with the aid of the Algorithm NSGAII to balance between two conflicting objectives: low weight and high endurance. It was found that it is possible to fly for more than 3 hours with a Maximum Take-off Weight of 21.6 kg, an 800 W fuel cell and 148 g of hydrogen. A heavier configuration with more power and fuel was discarded due to a wingspan constraint. Later, after the concept satisfied the project requirements, Multi-Disciplinary Design Optimisation (MDO) was performed to achieve the maximum endurance possible. The software used was OpenAeroStruct, low fidelity Finite Element Analysis (FEA) and Vortex Lattice Method (VLM) to model lifting surfaces. Initially, a cruise and a load flight point were used with wing geometric twist only as design variable. After, more complexity was added by introducing taper, wing chord and span. Finally, a third flight point was introduced to ensure the stall requirements were satisfied. The use of MDO allowed a 21% increase in endurance with a smaller wing area. Other improvements could not be achieved without violation of the constraints. This work marks an important milestone in the development of a future prototype at the Research Centre.N/

Multi-objective optimisation methods applied to complex engineering systems

This research proposes, implements and analyses a novel framework for multiobjective optimisation through evolutionary computing aimed at, but not restricted to, real-world problems in the engineering design domain. Evolutionary algorithms have been used to tackle a variety of non-linear multiobjective optimisation problems successfully, but their success is governed by key parameters which have been shown to be sensitive to the nature of the particular problem, incorporating concerns such as the number of objectives and variables, and the size and topology of the search space, making it hard to determine the best settings in advance. This work describes a real-encoded multi-objective optimising evolutionary algorithm framework, incorporating a genetic algorithm, that uses self-adaptive mutation and crossover in an attempt to avoid such problems, and which has been benchmarked against both standard optimisation test problems in the literature and a real-world airfoil optimisation case. For this last case, the minimisation of drag and maximisation of lift coefficients of a well documented standard airfoil, the framework is integrated with a freeform deformation tool to manage the changes to the section geometry, and XFoil, a tool which evaluates the airfoil in terms of its aerodynamic efficiency. The performance of the framework on this problem is compared with those of two other heuristic MOO algorithms known to perform well, the Multi-Objective Tabu Search (MOTS) and NSGA-II, showing that this framework achieves better or at least no worse convergence. The framework of this research is then considered as a candidate for smart (electricity) grid optimisation. Power networks can be improved in both technical and economical terms by the inclusion of distributed generation which may include renewable energy sources. The essential problem in national power networks is that of power flow and in particular, optimal power flow calculations of alternating (or possibly, direct) current. The aims of this work are to propose and investigate a method to assist in the determination of the composition of optimal or high-performing power networks in terms of the type, number and location of the distributed generators, and to analyse the multi-dimensional results of the evolutionary computation component in order to reveal relationships between the network design vector elements and to identify possible further methods of improving models in future work. The results indicate that the method used is a feasible one for the achievement of these goals, and also for determining optimal flow capacities of transmission lines connecting the bus bars in the network

New strategies for the aerodynamic design optimization of aeronautical configurations through soft-computing techniques

Premio Extraordinario de Doctorado de la UAH en 2013Lozano Rodríguez, Carlos, codir.This thesis deals with the improvement of the optimization process in the aerodynamic design of aeronautical configurations. Nowadays, this topic is of great importance in order to allow the European aeronautical industry to reduce their development and operational costs, decrease the time-to-market for new aircraft, improve the quality of their products and therefore maintain their competitiveness. Within this thesis, a study of the state-of-the-art of the aerodynamic optimization tools has been performed, and several contributions have been proposed at different levels: -One of the main drawbacks for an industrial application of aerodynamic optimization tools is the huge requirement of computational resources, in particular, for complex optimization problems, current methodological approaches would need more than a year to obtain an optimized aircraft. For this reason, one proposed contribution of this work is focused on reducing the computational cost by the use of different techniques as surrogate modelling, control theory, as well as other more software-related techniques as code optimization and proper domain parallelization, all with the goal of decreasing the cost of the aerodynamic design process. -Other contribution is related to the consideration of the design process as a global optimization problem, and, more specifically, the use of evolutionary algorithms (EAs) to perform a preliminary broad exploration of the design space, due to their ability to obtain global optima. Regarding this, EAs have been hybridized with metamodels (or surrogate models), in order to substitute expensive CFD simulations. In this thesis, an innovative approach for the global aerodynamic optimization of aeronautical configurations is proposed, consisting of an Evolutionary Programming algorithm hybridized with a Support Vector regression algorithm (SVMr) as a metamodel. Specific issues as precision, dataset training size, geometry parameterization sensitivity and techniques for design of experiments are discussed and the potential of the proposed approach to achieve innovative shapes that would not be achieved with traditional methods is assessed. -Then, after a broad exploration of the design space, the optimization process is continued with local gradient-based optimization techniques for a finer improvement of the geometry. Here, an automated optimization framework is presented to address aerodynamic shape design problems. Key aspects of this framework include the use of the adjoint methodology to make the computational requirements independent of the number of design variables, and Computer Aided Design (CAD)-based shape parameterization, which uses the flexibility of Non-Uniform Rational B-Splines (NURBS) to handle complex configurations. The mentioned approach is applied to the optimization of several test cases and the improvements of the proposed strategy and its ability to achieve efficient shapes will complete this study

New strategies for the aerodynamic design optimization of aeronautical configurations through soft-computing techniques

Premio Extraordinario de Doctorado de la UAH en 2013Lozano Rodríguez, Carlos, codir.This thesis deals with the improvement of the optimization process in the aerodynamic design of aeronautical configurations. Nowadays, this topic is of great importance in order to allow the European aeronautical industry to reduce their development and operational costs, decrease the time-to-market for new aircraft, improve the quality of their products and therefore maintain their competitiveness. Within this thesis, a study of the state-of-the-art of the aerodynamic optimization tools has been performed, and several contributions have been proposed at different levels: -One of the main drawbacks for an industrial application of aerodynamic optimization tools is the huge requirement of computational resources, in particular, for complex optimization problems, current methodological approaches would need more than a year to obtain an optimized aircraft. For this reason, one proposed contribution of this work is focused on reducing the computational cost by the use of different techniques as surrogate modelling, control theory, as well as other more software-related techniques as code optimization and proper domain parallelization, all with the goal of decreasing the cost of the aerodynamic design process. -Other contribution is related to the consideration of the design process as a global optimization problem, and, more specifically, the use of evolutionary algorithms (EAs) to perform a preliminary broad exploration of the design space, due to their ability to obtain global optima. Regarding this, EAs have been hybridized with metamodels (or surrogate models), in order to substitute expensive CFD simulations. In this thesis, an innovative approach for the global aerodynamic optimization of aeronautical configurations is proposed, consisting of an Evolutionary Programming algorithm hybridized with a Support Vector regression algorithm (SVMr) as a metamodel. Specific issues as precision, dataset training size, geometry parameterization sensitivity and techniques for design of experiments are discussed and the potential of the proposed approach to achieve innovative shapes that would not be achieved with traditional methods is assessed. -Then, after a broad exploration of the design space, the optimization process is continued with local gradient-based optimization techniques for a finer improvement of the geometry. Here, an automated optimization framework is presented to address aerodynamic shape design problems. Key aspects of this framework include the use of the adjoint methodology to make the computational requirements independent of the number of design variables, and Computer Aided Design (CAD)-based shape parameterization, which uses the flexibility of Non-Uniform Rational B-Splines (NURBS) to handle complex configurations. The mentioned approach is applied to the optimization of several test cases and the improvements of the proposed strategy and its ability to achieve efficient shapes will complete this study

Sensitivity analysis for multidisciplinary design optmization

When designing a complex industrial product, the designer often has to optimise simultaneously multiple conflicting criteria. Such a problem does not usually have a unique solution, but a set of non-dominated solutions known as Pareto solutions. In this context, the progress made in the development of more powerful but more computationally demanding numerical methods has led to the emergence of multi-disciplinary optimisation (MDO). However, running computationally expensive multi-objective optimisation procedures to obtain a comprehensive description of the set of Pareto solutions might not always be possible. The aim of this research is to develop a methodology to assist the designer in the multi-objective optimisation process. As a result, an approach to enhance the understanding of the optimisation problem and to gain some insight into the set of Pareto solutions is proposed. This approach includes two main components. First, global sensitivity analysis is used prior to the optimisation procedure to identify non- significant inputs, aiming to reduce the dimensionality of the problem. Second, once a candidate Pareto solution is obtained, the local sensitivity is computed to understand the trade-offs between objectives. Exact linear and quadratic approximations of the Pareto surface have been derived in the general case and are shown to be more accurate than the ones found in literature. In addition, sufficient conditions to identify non-differentiable Pareto points have been proposed. Ultimately, this approach enables the designer to gain more knowledge about the multi-objective optimisation problem with the main concern of minimising the computational cost. A number of test cases have been considered to evaluate the approach. These include algebraic examples, for direct analytical validation, and more representative test cases to evaluate its usefulness. In particular, an airfoil design problem has been developed and implemented to assess the approach on a typical engineering problem. The results demonstrate the potential of the methodology to achieve a reduction of computational time by concentrating the optimisation effort on the most significant variables. The results also show that the Pareto approximations provide the designer with essential information about trade-offs at reduced computational cost

Using Stochastic Dominance in Multi-Objective Optimizers for Aerospace Design Under Uncertainty

In optimization under uncertainty for aerospace design, statistical moments of the quan- tity of interest are often treated as separate objectives and are traded off in a multi-objective optimization formulation. However, in many design problems the trade-off between sta- tistical moments can be large and the Pareto front representing this trade-off can include designs with undesirable behavior, such as being robust but being guaranteed to give a worse performance than another design. When a simulation of a system is computation- ally expensive, obtaining the full Pareto front is unfeasible and so spending optimization time obtaining such undesirable designs wastes time that could be spent obtaining more desirable alternatives. As a remedy, we propose an optimization formulation that can use multiple dominance criteria to avoid generating potentially inferior designs. We consider various orders of stochastic dominance as criteria to use alongside statistical moment based Pareto dominance, and illustrate how this gives rise to improved designs using a limited computational budget in an acoustic horn design problem and a transonic airfoil design problem.EPSRC DTA grant, grant number EP/L504920/

Multi-Objective structural optimization of repairs of blisk blades

Modern manufacturing technologies offer multiple options to extend the service life of expensive jet engine components through repairs. In this context, the repair processes of blade-integrated disks (blisks) are of particular interest, as the complex design makes replacement of this part very costly. However, currently, repairs of blisks are mainly done manually and repair design decisions still rely on the expertise of maintenance technicians. From a scientific perspective, these subjective, experience-based decisions are a major drawback, as today’s computational methods allow for systematic analysis and evaluation of design alternatives. The present doctoral thesis contributes to the decision-making process related to the repair of blisk blades by blending and patching by providing an engineering optimization framework and simulation routines for structural assessment of different repair designs. First, an object-oriented optimization framework is developed that is ideally suited to address engineering optimization problems such as blisk repair optimization. The design of the software architecture is chosen to achieve a high degree of flexibility and modularity. In particular, the framework provides a unified interface for global and local derivative-free optimization algorithms and custom engineering optimization problems. Thereby, optimization of single- as well as multi-objective problems is supported. The broad applicability of the framework in engineering optimization is demonstrated using examples from wind energy research. Furthermore, the optimization framework forms a suitable environment for structural multi-objective optimization of blend and patch repairs. The second part of this thesis is devoted to the application of the optimization framework to blend repairs of a compressor blisk. The geometry of the removed blade part and the resulting blend is parameterized by three geometric design variables. The two objectives of the optimization correspond to two modal criteria, because especially the vibration behavior of blades is affected by this kind of geometric modification. To check if frequency requirements are harmed by the repair the first objective reflects the deviation of the natural frequencies of the repaired blade to the natural frequencies of the nominal blade. The second objective considers resonance conditions by evaluating the proximity of natural frequencies to excitation frequencies. Pareto optimal repair designs are found by solving the derived optimization problem using appropriate structural mechanics models of a blade sector and employing the developed optimization framework. By analyzing the optimal blend shapes for two different damage patterns, it is shown that the characteristics of Pareto frontiers, like the occurrence of discontinuities, are damage-specific. Therefore, it is concluded that design decisions on blend repairs have to be made on a case-by-case basis. The third part of this thesis is concerned with the multi-objective optimization of patch repairs. While blend repairs change the blade geometry, patch repairs restore the original blade contour. In terms of structural integrity, the most significant modification due to patching is hence associated with the welding process to join patch and blade. The remaining residual stresses, affect the strength of the repaired blade, are therefore the most critical aspect of patch repairs. Utilizing the engineering optimization framework and the parametric simulation model, a multi-objective optimization problem is solved considering the length of the weld and the fatigue strength of the repaired blade. In addition to fatigue strength properties, the weld length is selected as an optimization goal, since the manufacturing effort of the high-tech repair is of practical importance. Pareto optimal repair designs are presented for a damage pattern at the leading edge. The optimization results are further complemented by subsequent thermal and mechanical simulations of the welding and heat treatment process. Different patch geometries are classified from the Pareto optimal solutions. Depending on the preferences in terms of weld length and the High-Cycle Fatigue strength of different load cases, short or long patches are to be used. In addition, the results show that some potential patch designs are not optimal in any case, and therefore can be completely excluded. Finally, the benefits of the unified interface of the engineering optimization framework are emphasized. Different optimization settings of a patch repair optimization are presented and compared utilizing the hypervolume metric. Concluding remarks on the potential of computational methods for improved repair design and an outlook on future maintenance of blisks complete this work.DFG/SFB 871/119 193 472./E

Optimization using multiple dominance criteria for aerospace design under uncertainty

In optimization under uncertainty for aerospace design, statistical moments of the quantity of interest are often treated as separate objectives and are traded off in a multi-objective optimization formulation. However, in many design problems the trade-off between statistical moments can be large and the Pareto front representing this trade-off can include designs with undesirable behavior, such as being robust but being guaranteed to give a worse performance than another design. When a simulation of a system is computationally expensive, obtaining the full Pareto front is infeasible and so spending optimization time obtaining such undesirable designs wastes time that could be spent obtaining more desirable alternatives. As a remedy, we propose an optimization formulation that can use multiple dominance criteria to avoid generating potentially inferior designs. We consider various orders of stochastic dominance as criteria to use alongside statistical moment based Pareto dominance, and illustrate how this gives rise to improved designs using a limited computational budget in an acoustic horn design problem and a transonic airfoil design problem.This work is part funded by the Engineering and Physical Sciences Research Council (EPSRC) UK, under grant number EP/L504920/1, with support from the Air Force Office of Scientific Research (AFOSR) MURI on managing multiple information sources of multi-physics systems, Program Manager Jean-Luc Cambier, Award Number FA9550-15-1-003