In order to fulfill increasingly stringent design criteria, designers may need to consider more advanced engineering materials. One way to improve the performance of materials is to combine different monolithic materials in such a way as to capture the best qualities of both. Such combined, heterogeneous materials are known as multi-materials or hybrid materials. Fiber-reinforced materials and sandwich structures are examples. Selection methodologies and tools for selecting monolithic materials are well established and widely used, but less is known about the design and selection of multi-materials. Here we develop a systematic selection methodology and tool to identify promising solutions, focusing on material selection for foam-core sandwich beams. Two approaches are developed in this study: a real route and a virtual route, pursuing three design objectives: to minimize mass, to minimize cost and to minimize heat transfer. The results of both approaches are compared and discussed. A selection example is also presented to illustrate the use of this tool.@en

This paper introduces Metamorphic Development (MD), a novel topology optimization method for truss structures with discrete member lengths and sizes. The method enables a structure to develop through both growth and degeneration towards an optimal topology, minimizing structural compliance and mass subject to constraints on displacement and stress. In contrast to ground structure based approaches, the optimization can start from a very simple initial structure which defines and connects the applied loads and support points using a minimal number of members. The structure is then developed metamorphically in a specified design domain using truss members of predefined sizes. The examples presented demonstrate the potential of this method to generate innovative solutions to structural design optimization problems in a very computationally efficient manner.@en

The complexity of modern gas turbine engines has led to the adoption of a modular design approach, in which a conceptual design phase fixes the values for a number of parameters and dimensions in order to facilitate the subdivision of the overall task into a number of simpler design problems. While making the overall problem more tractable, the introduction of these process-intrinsic constraints (such as flow areas and radii between adjacent stages) at a very early phase of the design process can limit the level of performance achievable, neglecting important regions of the design space and concealing important trade-offs between different modules or disciplines. While this approach has worked satisfactorily in the past, the continuous increase in components' efficiencies and performance makes further advances more difficult to achieve. Part I of this paper described the development of a system for the integrated design optimization of gas turbine engines: postponing the setting of the interface constraints to a point where more information is available facilitates better exploration of the available design space and better exploitation of the trade-offs between different disciplines and modules. In this second part of the paper, the proposed approach is applied to several test cases from the design of a three-spool gas turbine engine core compression system, demonstrating the risks associated with a modular design approach and the consistent gains achievable through the proposed integrated optimization approach.@en

The design of gas turbine engines is a complex problem. This complexity has led to the adoption of a modular design approach, in which a conceptual design phase fixes the values for some global parameters and dimensions in order to facilitate the subdivision of the overall task into a number of simpler subproblems. This approach, while making a complex problem more tractable, necessarily has to rely on designer experience and simple evaluations to specify these process-intrinsic constraints at a point in the design process where very little knowledge about the final design exists. Later phases of the design process, using higher-fidelity tools but acting on a limited region of the design space, can only refine an already established design. While substantial improvements in performance have been possible with the current approach, further gains are becoming increasingly hard to achieve. A gas turbine is a complex multidisciplinary system: a more integrated design approach can facilitate a better exploitation of the trade-offs between different modules and disciplines, postponing the setting of these critical interface parameters (such as flow areas, radii, etc.) to a point where more information exists, reducing their impact on the final design. In the resulting large, possibly multimodal, highly constrained design space, and with a large number of objectives to be considered simultaneously, finding an optimal solution by simple trial-and-error can prove extremely difficult. A more intelligent search approach, in which a numerical optimizer takes the place of the human designer in seeking optimal designs, can enable the design space to be explored significantly more effectively, while also yielding a substantial reduction in development times thanks to the automation of the design process. This paper describes the development of a system for the integrated design and optimization of gas turbine engines, linking a metaheuristic optimizer to a geometry modeler and to evaluation tools with different levels of fidelity. In recognition of the substantial increase in design space size required by the integrated approach, an improved parameterization based on the concept of principal components' analysis was implemented, allowing a rotation of the design space along its most significant directions and a reduction in its dimensionality, proving essential for a faster and more effective exploration of the design space.@en

The design of a Hybrid Electric Vehicle (HEV) system is an energy management strategy problem between two sources of power. Traditionally, the drive train has been designed first, and then a driving strategy chosen and sometimes optimised. This paper considers the simultaneous optimisation of both drive train and driving strategy variables of the HEV system through use of a multi-objective evolutionary optimiser. The drive train is well understood. However, the optimal driving strategy to determine efficient and opportune use of each prime mover is subject to the driving cycle (the type of dynamic environment, e.g. urban, highway), and has been shown to depend on the correct selection of the drive train parameters (gear ratios) as well as driving strategy heuristic parameters. In this paper, it is proposed that the overall optimal design problem has to consider multiple objectives, such as fuel consumption, reduction in electrical energy stored, and the 'driveability' of the vehicle. Numerical results shows improvement when considering multiple objectives and simultaneous optimisation of both drive train and driving strategy.@en

An effective optimization procedure for finding structural shapes and topologies that minimize structural compliance and weight subject to stress and deflection constraints is presented. This new approach, called `Metamorphic Development' (MD), can allow a structure to grow and degenerate towards an optimum topological layout. In this method, the optimization can start from the simplest possible geometry (layout) or any degree of development of the structure rather than from a complex ground mesh. The structure is then developed metamorphically using rectangular and triangular elements that can be of any specified sizes. Examples demonstrate the potential of the MD optimization procedure to generate innovative solutions to structural design problems. Results are given and the growth and degeneration histories during optimization are illustrated.@en

This paper introduces a new technique called species conservation for evolving parallel subpopulations. The technique is based on the concept of dividing the population into several species according to their similarity. Each of these species is built around a dominating individual called the species seed. Species seeds found in the current generation are saved (conserved) by moving them into the next generation. Our technique has proved to be very effective in finding multiple solutions of multimodal optimization problems. We demonstrate this by applying it to a set of test problems, including some problems known to be deceptive to genetic algorithms.@en

Using the design of bicycle frames as a case study, this paper explores the potential of a multiobjective extension of the shape annealing approach to conceptual design. The key elements of this approach are a randomized search based optimization method (to simulate creativity), a generative structural shape grammar (to allow different configurations to be explored), and a multiobjective optimization approach (to identify competing concepts occupying different parts of the trade-off surface). The results presented demonstrate the success of this approach in exploring a multiplicity of different design configurations and presenting the designer with a variety of Pareto-optimal concepts worthy of further consideration.@en

This paper presents an investigation into the motion of two-wheelers: Everyday motorcycles and bicycles. The emphasis is on controllability of the system for small lateral deviations from straight running under idealized rider control. After introduction, a discussion of the kinematics, assumptions and geometry of a rider-vehicle system is presented, followed by a statement of the equations of motion. The control systems analogy is briefly reviewed, and state space methods formalize the concept of controllability. The difficulty in steered riding is quantified by the ratio of maximum to minimum singular values of the controllability Grammian and rideability is investigated for different designs of (a) a motorcycle from a well-known study and (b) a bicycle from a recent investigation. New insight into controlled two-wheeler behaviour is shown, compared with traditional methods, and can provide another means to design for a safety of vehicle performance.@en

An approach to support the computational aerodynamic design process is presented and demonstrated through the application of a novel multi-objective variant of the Tabu Search optimization algorithm for continuous problems to the aerodynamic design optimization of turbomachinery blades. The aim is to improve the performance of a specific stage and ultimately of the whole engine. The integrated system developed for this purpose is described. This combines the optimizer with an existing geometry parameterization scheme and a well-established CFD package. The system's performance is illustrated through case studies - one two-dimensional, one three-dimensional - in which flow characteristics important to the overall performance of turbomachinery blades are optimized. By showing the designer the trade-off surfaces between the competing objectives, this approach provides considerable insight into the design space under consideration and presents the designer with a range of different Pareto-optimal designs for further consideration. Special emphasis is given to the dimensionality in objective function space of the optimization problem, which seeks designs that perform well for a range of flow performance metrics. The resulting compressor blades achieve their high performance by exploiting complicated physical mechanisms successfully identified through the design process. The system can readily be run on parallel computers, substantially reducing wall-clock run times - a significant benefit when tackling computationally demanding design problems. Overall optimal performance is offered by compromise designs on the Pareto trade- off surface revealed through a true multi-objective design optimization test case. Bearing in mind the continuing rapid advances in computing power and the benefits discussed, this approach brings the adoption of such techniques in real-world engineering design practice a step closer.@en

As an extension of the Evolutionary Structural Optimization [ESO] method, the bidirectional ESO [BESO] method has effectively addressed various topology optimization problems. It is observed in ESO/BESO applications that the optimal solution obtained strongly depends on the finite element mesh. This paper presents an improved BESO methodology incorporating a means of controlling the optimization process in order to satisfy a constraint on structural perimeter and thus to solve this size effect problem. Numerical tests are conducted on three examples at different levels of finite element discretization. Solutions convergent with respect to the grid refinement are obtained, especially when the perimeter bound is sufficiently low. Simpler topologies consisting of fewer and larger structural members and holes are generated when a more restricting constraint is imposed. Therefore, it is concluded that BESO combined with perimeter control is capable of suppressing mesh dependency and controlling the structural complexity for topology optimization problems.@en

While there have been many adaptations of some of the more popular meta-heuristics for continuous multi-objective optimisation problems, Tabu Search has received relatively little attention, despite its suitability and effectiveness on a number of real-world design optimisation problems. In this paper we present an adaptation of a single-objective Tabu Search algorithm for multiple objectives. Further, inspired by path relinking strategies common in discrete optimisation problems, we enhance our algorithm to allow it to handle problems with large numbers of design variables. This is achieved by a novel parameter selection strategy that, unlike a full parametric analysis, avoids the use of objective function evaluations, thus keeping the overall computational cost of the procedure to a minimum. We assess the performance of our two Tabu Search variants on a range of standard test functions and compare it to a leading multi-objective Genetic Algorithm, NSGA-II. The path relinking-inspired parameter selection scheme gives a clear performance improvement over the basic multi-objective Tabu Search adaptation and both variants perform comparably with the NSGA-II.@en

The selection of a material to meet given design requirements generally requires that a compromise be struck between several, usually conflicting, objectives. The problem is complicated because the decision-space is large, it is discrete rather than continuous, and the relative value to be placed on each objective is imprecisely known. Here we explore the ways in which multi-objective optimisation methods can be adapted to address this problem. We find that trade-off surfaces give a way of visualizing the alternative compromises, and that "utility" functions (or "value" functions) identify the part of the surface on which optimal solutions lie. Implementing this for two objectives is straightforward, but doing so for more then two requires new visualization tools. Here we develop a tool and illustrate its use.@en

A novel topology/shape optimisation method for axisymmetric elastic solids, based on solid modeling and FE analysis, is presented. Optimal profiles of minimum-mass axisymmetric structures are sought by growing and degenerating simple initial structures subject to response constraints. The rates of the growth and degeneration are controlled based on the current objective and constraint functions of the optimisation problem under consideration. The optimal structures are developed metamorphically in specified infinite design domains using both quadrilateral and triangular axisymmetric finite elements that are ideally suited for modeling continua involving curved boundaries. The robustness of this fully automatic method is studied and validated with the first example of seeking the optimal shape of a centrally suspended axisymmetric object with minimum strain energy caused by self-weight. Then the method is applied to a practical industrial design problem: the design of a turbine disk. The variations of load and boundary conditions caused by shape change in these problems, including the gravitational and centrifugal loads, and temperature distribution are accommodated in the optimisation procedures. Thus, the design model closely resembles the real design problem. The results demonstrate the success of the method in generating optimal but realistic solutions to practical design problems.@en

In this study, optimal shapes of intersecting pressure vessels are sought using a novel topology/shape optimisation method, called Metamorphic Development (MD). An industrial benchmark design problem of finding the optimal profile of variable thickness that connects a spherical shell pressure vessel to a cylindrical nozzle is considered. Two types of intersecting structures, distinguished by flush and protruding nozzles, are investigated. The optimum profiles of minimum mass intersecting structures are found by growing and degenerating simple initial structures subject to stress constraints. The optimisation seeks to eliminate the stress peaks caused by the opening. The optimised structures are developed metamorphically in specified infinite design domains using both rectangular and triangular axisymmetric finite elements that are ideally suited for modelling continua with curved boundaries. It is shown that the design with a protruding nozzle would produce a better stress distribution than the design with a flush nozzle. The results demonstrate the success of the method in generating suitable, practical solutions to the design problem.@en

In real-world optimization problems, large design spaces and conflicting objectives are often combined with a large number of constraints, resulting in a highly multi-modal, challenging, fragmented landscape. The local search at the heart of Tabu Search, while being one of its strengths in highly constrained optimization problems, requires a large number of evaluations per optimization step. In this work, a modification of the pattern search algorithm is proposed: this modification, based on a Principal Components' Analysis of the approximation set, allows both a re-alignment of the search directions, thereby creating a more effective parametrization, and also an informed reduction of the size of the design space itself. These changes make the optimization process more computationally efficient and more effective - higher quality solutions are identified in fewer iterations. These advantages are demonstrated on a number of standard analytical test functions (from the ZDT and DTLZ families) and on a real-world problem (the optimization of an axial compressor preliminary design).@en

In the last 15 years, automatic design optimisation has been the subject of ever growing interest, thanks to the development of ever more reliable analysis software, efficient optimisation methods and powerful computers. Even in industrial environments, design optimisation is extensively used in a number of disciplines, such as aerodynamics, structures and many more applications. Better designs in shorter times and clearer trade-offs between different objectives and disciplines are the most generally recognised advantages.22 The parameterisation represents the " critical enabling factor" for an efficient exploration of the design space: it is essential to ensure that the parameterisation scheme is able to cover all feasible designs, in order not to lose potentially good designs, but also that the minimum possible number of parameters is used, since these affect the size of the design space and thus the convergence time of the optimiser. Irrespective of the specific parameterisation technique, the optimisation of complex products is likely to translate into a large design space and an a priori reduction is not advisable, as this could reduce the generality of the paramenterisation and lead to the loss of potentially good designs. Kipouros et al.16 have presented a method for selecting only the most significant components based on the results of a preliminary optimisation run. In the present study, a method based on Principal Components' Analysis is introduced: given a generic parameterisation, this allows an optimal representation to be derived that will facilitate a faster and more complete exploration of the design space. The advantages of this approach are demonstrated through two optimisation test cases from the design of a core compression system for a three-spool modern turbofan engine.@en

The design of a gas turbine, or one of its constituent modules, is generally approached with some specific operating condition in mind (its design point). Unfortunately, engine components seldom exactly meet their specifications and do not operate at just one condition, but over a range of power settings. This simplification can then lead to a product that exhibits performance worse than nominal in real-world conditions. The integration of some consideration of robustness as an active part of the design process can allow products less sensitive to the presence of the noise factors commonly found in real-world environments to be obtained. To become routinely used as a design tool, minimization of the time required for robustness analysis is paramount. In this study, a nonintrusive polynomial chaos formulation is used to evaluate the variability in the performance of a generic modular-core compression system for a three-spool modern gas turbine engine subject to uncertain operating conditions with a defined probability density function. The standard orthogonal polynomials from the Askey scheme are replaced by a set of orthonormal polynomials calculated relative to the specific probability density function, improving the convergence of the method.@en

At present, optimization is an enabling technology in innovation. Multi-objective and multidisciplinary optimization tools are essential in the design process for real-world applications. In turbomaehinery design, these approaches give insight into the design space and identify the tradeoffs between the competing performance measures. This paper describes the application of a novel multi-objective variant of the tabu search algorithm to the aerodynamic design optimization of turbomachinery blades. The aim is to improve the performance of a specific stage and eventually of the whole engine. The integrated system developed for this purpose is described. It combines the optimizer with an existing geometry parameterization scheme and a well-established computational fluid dynamics package. Its performance is illustrated through a case study in which the flow characteristics most important to the overall performance of turbomachinery blades are optimized.@en