Gas turbine compression systems are required to perform adequately over a range of operating conditions. Complexity has encouraged the conventional design process for compressors to focus initially on one operating point, usually the most commonor arduous, to draw up an outline design. Generally, only as this initial design is refined is its offdesign performance assessed in detail. Not only does this necessarily introduce a potentially costly and timeconsuming extra loop in the design process, but it also may result in a design whose offdesign behavior is suboptimal. Aversion of nonintrusive polynomial chaos was previously developed in which a set of orthonormal polynomials was generated to facilitate a rapid analysis of robustness in the presence of generic uncertainties with good accuracy. In this paper, this analysis method is incorporated in real time into the design process for the compression system of a three-shaft gas turbine aeroengine. This approach to robust optimization is shown to lead to designs that exhibit consistently improved system performance with reduced sensitivity to offdesign operation.

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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.

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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.

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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.

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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

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.

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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

Engineering design commonly assumes nominal values for uncertain parameters to simplify the design process: the design of a gas turbine, or one of its modules, is generally approached with some specific operating conditions in mind (its design point). Unfortunately, engine components never 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 significantly worse than nominal in real-world conditions. This problem is exacerbated in the presence of heavily optimised designs, which tend to lie in extreme regions of the design space.15 In gas turbine design, safe and satisfactory off-design operation must be guaranteed and is generally evaluated before moving to the next phase of the design process. This approach, while guaranteeing that some minimum requirements are met, introduces a further loop in the design process and does not ensure the final design will be optimal with respect to this new requirement. The introduction of some robustness considerations into the design process can reduce the level of fragmentation and iteration typical of gas turbine engine design and produce further (and more robust) improvements relative to the traditional method. In this study, two approaches for dealing with off-design performance analysis are presented, integrated into an automatic optimisation system and applied to the preliminary design of a core compression system from a three-spool modern turbofan engine. Designs that are more robust than those found if only design-point performance is considered are successfully identified.@en

Given the focus on incremental change in existing empirical aerodynamic design methods, radical, unintuitive, new optimal solutions in previously unexplored regions of design space are very unlikely to be found using them. We present a framework based on an implicit shape representation and a multiobjective evolutionary algorithm that aims to produce a variety of optimal flow topologies for a given requirement, providing designers with insights into possibly radical solutions. A revolutionary integrated flow simulation system developed specifically for design work is used to evaluate candidate designs.@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

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

We present a novel framework for robust aerodynamic design optimization with respect to CFD modeling errors using multi-fidelity simulations, a multi-objective optimization algorithm, and a surrogate model employed to map the error landscape across the design space. We use the low- and high-fidelity CFD model divergence as a proxy for simulation risk, which is simultaneously optimized along with a measure of performance. Instead of generating high-fidelity simulations directly, we employ a Sparse Pseudo-input Gaussian Process surrogate modeling algorithm to predict the divergence. We apply this approach to a simple diffuser design problem, coupled with a multi-objective Tabu Search optimization algorithm, which shows encouraging results. We are able to generate a range of Pareto optimal design, which display a trade-off between aerodynamic performance and simulation risk. This approach is applicable to more general problems and would be of interest in an industrial design setting.

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Modern turbofan engines are designed with pressure ratios as high as 40 and with bypass ratios in excess of 8. Multiple spools with substantial radial offset are essential to achieve the desired design and off-design performance and s-shaped ducts are necessary to deliver the flow from the exit of a turbomachine to the inlet of the following one in the minimum possible space to reduce the weight and the size of the gas turbine, without the risk of incurring in flow separation. In the absence of practical design rules or performance correlations for annular s-shaped ducts, a practical design approach could be the use of Computational Fluid Dynamics (CFD) for performance evaluation together with optimisation techniques for seeking the best design. Numerical optimisation methods (either deterministic or stochastic) can be linked to CFD solvers to provide a more thorough exploration of the design space, trying to produce a better design than the datum one, subject to a number of constraints. This paper reports the development and testing of an automatic framework for design optimisation of s-shaped ducts and its initial application to the optimisation of an axial-symmetric inter-compressor duct.

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The reliance of Tabu Search (TS) algorithms on a local search leads to a logical development of algorithms that use more than one search concurrently. In this paper we present a multi-threaded TS algorithm employing a number of threads that share information. We assess the performance of this algorithm compared to previous multi-objective TS algorithms, via the results obtained from applying the algorithms to a range of standard test functions. We also consider whether an optimal number of threads can be found, and what impact changing the number of threads used has on performance. We discover that, contrary to the popular belief that multi-threading is usually beneficial, performance only improves in a few special cases.

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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.

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A tool to support designers in comparing the performances of multi-materials with those of other materials and to guide their selection for a given application is discussed. Particulate and fibrous composites can be included in a materials database, allowing direct comparison and selection by established material selection methodologies in the catalogue approach. A common design strategy for multi-materials is to tailor them to fulfill the design requirements as losely as possible by varying either constituents, configuration or scale. The basis for the selection of materials in forming multi-materials is to use the desirable attributes of one monolithic material to compensate for the inadequate attributes of others.@en

Real-world engineering optimisation problems are typically multi-objective and highly constrained, and constraints may be both costly to evaluate and binary in nature. In addition, objective functions may be computationally expensive and, in the commercial design cycle, there is a premium placed on rapid initial progress in the optimisation run. In these circumstances, evolutionary algorithms may not be the best choice; we have developed a multi-objective Tabu Search algorithm, designed to perform well under these conditions. Here we present the algorithm along with the constraint handling approach, and test it on a number of benchmark constrained test problems. In addition, we perform a parametric study on a variety of unconstrained test problems in order to determine the optimal parameter settings. Our algorithm performs well compared to a leading multi-objective Genetic Algorithm, and we find that its performance is robust to parameter settings.

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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

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