András Sóbester

Multi-fidelity optimization via surrogate modelling

This paper demonstrates the application of correlated Gaussian process based approximations to optimization where multiple levels of analysis are available, using an extension to the geostatistical method of co-kriging. An exchange algorithm is used to choose which points of the search space to sample within each level of analysis. The derivation of the co-kriging equations is presented in an intuitive manner, along with a new variance estimator to account for varying degrees of computational ‘noise’ in the multiple levels of analysis. A multi-fidelity wing optimization is used to demonstrate the methodology.

On the Design of Optimization Strategies Based on Global Response Surface Approximation Models

Striking the correct balance between global exploration of search spaces and local exploitation of promising basins of attraction is one of the principal concerns in the design of global optimization algorithms. This is true in the case of techniques based on global response surface approximation models as well. After constructing such a model using some initial database of designs it is far from obvious how to select further points to examine so that the appropriate mix of exploration and exploitation is achieved. In this paper we propose a selection criterion based on the expected improvement measure, which allows relatively precise control of the scope of the search. We investigate its behavior through a set of artificial test functions and two structural optimization problems. We also look at another aspect of setting up search heuristics of this type: the choice of the size of the database that the initial approximation is built upon.

Tradeoffs in Jet Inlet Design: A Historical Perspective

The design of the inlet(s) is one of the most demanding tasks of the development process of any gas turbine-powered aircraft. This is mainly due to the multi-objective and multidisciplinary nature of the exercise. The solution is generally a compromise between a number of conflicting goals and these conflicts are the subject of the present paper. We look into how these design tradeoffs have been reflected in the actual inlet designs over the years and how the emphasis has shifted from one driver to another. We also review some of the relevant developments of the jet age in aerodynamics and design and manufacturing technology and we examine how they have influenced and informed inlet design decisions

Aircraft aerodynamic design : geometry and optimization

Optimal aircraft design is impossible without a parametric representation of the geometry of the airframe. We need a mathematical model equipped with a set of controls, or design variables, which generates different candidate airframe shapes in response to changes in the values of these variables. This models objectives are to be flexible and concise, and capable of yielding a wide range of shapes with a minimum number of design variables. Moreover, the process of converting these variables into aircraft geometries must be robust. Alas, flexibility, conciseness and robustness can seldom be achieved simultaneously. Aircraft Aerodynamic Design: Geometry and Optimization addresses this problem by navigating the subtle trade-offs between the competing objectives of geometry parameterization. It beginswith the fundamentals of geometry-centred aircraft design, followed by a review of the building blocks of computational geometries, the curve and surface formulations at the heart of aircraft geometry. The authors then cover a range of legacy formulations in the build-up towards a discussion of the most flexible shape models used in aerodynamic design (with a focus on lift generating surfaces). The book takes a practical approach and includes MATLAB®, Python and Rhinoceros® code, as well as ‘real-life’ example case studies

Genetic Programming Approaches for Solving Elliptic Partial Differential Equations

In this paper, we propose a technique based on genetic programming (GP) for meshfree solution of elliptic partial differential equations. We employ the least-squares collocation principle to define an appropriate objective function, which is optimized using GP. Two approaches are presented for the repair of the symbolic expression for the field variables evolved by the GP algorithm to ensure that the governing equations as well as the boundary conditions are satisfied. In the case of problems defined on geometrically simple domains, we augment the solution evolved by GP with additional terms, such that the boundary conditions are satisfied by construction. To satisfy the boundary conditions for geometrically irregular domains, we combine the GP model with a radial basis function network. We improve the computational efficiency and accuracy of both techniques with gradient boosting, a technique originally developed by the machine learning community. Numerical studies are presented for operator problems on regular and irregular boundaries to illustrate the performance of the proposed algorithms.

Optimization with missing data

Engineering optimization relies routinely on deterministic computer based design evaluations, typically comprising geometry creation, mesh generation and numerical simulation. Simple optimization routines tend to stall and require user intervention if a failure occurs at any of these stages. This motivated us to develop an optimization strategy based on surrogate modelling, which penalizes the likely failure regions of the design space without prior knowledge of their locations. A Gaussian process based design improvement expectation measure guides the search towards the feasible global optimum.

A comprehensive preference-based optimization framework with application to high-lift aerodynamic design

An integral component of transport aircraft design is the high-lift configuration, which can provide significant benefits in aircraft payload-carrying capacity. However, aerodynamic optimization of a high-lift configuration is a computationally challenging undertaking, due to the complex flow-field. The use of a designer-interactive multiobjective optimization framework is proposed, which identifies and exploits preferred regions of the Pareto frontier. Visual data mining tools are introduced to statistically extract information from the design space and confirm the relative influence of both variables and objectives to the preferred interests of the designer. The framework is assisted by the construction of time-adaptive Kriging models, which are cooperatively used with a high-fidelity Reynolds-averaged Navier–Stokes solver. The successful integration of these design tools is facilitated through the specification of a reference point, which can ideally be based on an existing design configuration. The framework is demonstrated to perform efficiently for the present case-study within the imposed computational budget.

Conceptual design of UAV airframes using a generic geometry service

With the increased freedom in layout selection possible when designing an Unmanned Air Vehicle (UAV) concept (compared, for example, to the relatively constrained and mature world of commercial airliner design), comes the significant challenge of building a geometry engine that will provide the variety of airframe models demanded by the highly global nature of the design search. In order to enable multidisciplinary trade-off studies, both an external surface and an internal structure are required – we use a single, generic model to supply these, in the form of a parametric geometry residing in a commercial CAD tool. In addition to discussing the challenges of offering a truly flexible geometry service, we also delve into the UAV-specific issues of the initial sizing of the model. A wealth of statistical data provides one of the traditional handholds for this step in manned aircraft conceptual design – we discuss the applicability of such statistical approaches to their unmanned counterparts.

Swarm Heuristic for Identifying Preferred Solutions in Surrogate-Based Multi-Objective Engineering Design

Exploring the entire Pareto frontier of high-fidelity multidisciplinary problems can be prohibitive due to the excessive number of expensive evaluations required. The use of surrogate models offers promise toward managing such problems, which are restricted by a computational budget. In this paper, the kriging-assisted user-preference multi-objective particle swarm heuristic is presented, in which less accurate but inexpensive surrogate models are used cooperatively with the precise but expensive objective functions to alleviate the computational burden. A userpreference module is integrated into the optimization framework, which guides the swarm toward preferred regions of the Pareto frontier, thereby focusing all computing effort on identifying only solutions of interest to the designer. While providing a logical criterion to prescreen candidates for precise evaluation, the additional guidance provided by user-preferences guarantees an accelerated convergence rate. To depict the proficiency of the proposed framework, a suite of test problems, including the multidisciplinary cross-sectional design of a semimonocoque fuselage enclosing a pressurized cabin and payload bay, is presented.Aparametric model is described that is capable of generating a broad range of double-lobe fuselage designs. The superiority of the kriging-assisted user-preference multi-objective particle swarm optimization algorithm over more traditional search methods to efficiently manage high-fidelity discontinuous design problems is highlighted.

Multidisciplinary design optimization of UAV airframes

If one considers the problem of converting an aircraft mission profile into an airframe design from an optimization theory perspective, it becomes obvious that the search problem comes with all the trimmings. The design space is large and multidimensional, there are multiple and often highly multimodal objectives and constraints, these depending not only on the design variables, but often on each other as well. Multidisciplinary Design Optimization studies can be conducted at different levels of detail, depending on the chosen trade-off between the size of the design space and the fidelity of the analysis. In this paper we discuss some of the challenges arising at the conceptual level, where simple, but versatile models and low cost analysis tools are used to guide the designer through the first, fundamental decisions of the design process. At the centre of our proposed design workflow lies a parametric geometry, residing in an off-the-shelf Computer-Aided Design (CAD) tool - this provides the models required by the multidisciplinary analyses. We also touch on some of the issues specific to the design of our chosen class of aircraft - Unmanned Air Vehicles (UAVs). To summarize: a CAD-based UAV conceptual design framework is proposed and demonstrated.