An adjoint for likelihood maximization

The process of likelihood maximization can be found in many different areas of computational modelling. However, the construction of such models via likelihood maximization requires the solution of a difficult multi-modal optimization problem involving an expensive O(n3) factorization. The optimization techniques used to solve this problem may require many such factorizations and can result in a significant bottle-neck. This article derives an adjoint formulation of the likelihood employed in the construction of a kriging model via reverse algorithmic differentiation. This adjoint is found to calculate the likelihood and all of its derivatives more efficiently than the standard analytical method and can therefore be utilised within a simple local search or within a hybrid global optimization to accelerate convergence and therefore reduce the cost of the likelihood optimization

Aircraft cost modelling, integrated in a multidisciplinary design context

Most of the current cost models focus on a particular manufacturing process or a specific maintenance aspect, therefore not providing the whole picture. The main challenge in modelling the manufacturing cost, associated to a new aircraft at the initial design stage, is to examine all the cost features and the way to link them into the decision making process. It is important to understand the cost related to different competing designs, and this can be tackled by including cost estimation in the design process. Estimating the cost at the early design stage is paramount to reduce the life cycle cost of the aircraft. This paper presents the development of a new methodology for the generation of a cost estimation approach for preliminary aircraft design in a multidisciplinary environment. The framework is able to capture the design attributes that drive the cost allowing a designer to assess cost changes with respect to different design configurations. The cost model is built in Excel using a Visual Basic interface and it is integrated within Model Centre platform, where it can be treated as a component of a computational design process. The paper concludes by presenting the results from a real wing trade-off study that includes all the components of a complete design system

Visualization methodologies in aircraft design

This paper reviews aspects of low dimensional visualization methods, which are used currently in aerodynamic design and how these can be extended to higher dimensions. The shortcomings in current visualization methods are described and methods introduced which extend other visualization methods to this application. These simplify complex ideas into a small number of plots that the designer can understand and so use to gain insight into design. In general these take the form of maps which reduce the problem dimensionality from 5 and 8D to just 2 dimensions. This enables screening and optimization to be performed visually. Much of this is made possible only because the large amounts of data required for high dimensional design space appreciation are provided by response surface method technology. A modus operandi is proposed and the possibilities for visualization as an aid to understanding design are illustrated via aircraft aerodynamic design. Application to a sample problem that deals with a military aircraft optimization problem in 2, 5, 8 and 14 dimensions is discussed

Visualization methodologies in aircraft design optimization

This thesis reviews aspects of current low dimensional visualisation methods which are useful in design and how these can be extended to higher dimensions.  The deficiencies in these methods are described and new visualisation methods are introduced, which simplify complex ideas into a small number of plots, that the designer can understand and to use to gain insight into design.  Much of this is made possible only because the large amounts of data required for high dimensional design space appreciation are provided by response surface method technology.  A modus operandi is proposed and the possibilities for visualisation as an aid to understanding design are studies in aircraft aerodynamic design.  Sample problems include analytical functions, such as a two dimensional bump problem and a military aircraft optimisation problem in 5, 8 and 14 dimensions. The new visualisation methodologies introduced are utilised to support design decisions for the sample design problems, such as the relative scaling of the design variables and constraints and choice of penalty function, which are important in optimisation.  Also extended is the potential to recognise problems such as numerical noise and boundaries of evaluation failure.  Initial design of experiments are shown to be improved in a systematic way by calculation of additional points dictated by maps of statistical and other error criteria. Although this technology is developed with reference to aircraft conceptual and aerodynamic design in particular, the design space visualisation and curve-fitting technology developed is general.  It should therefore be equally applicable to other disciplines such as cost analysis, structures and computational electromagnetics, in which expensive analysis tools are used to find optima for complicated design problems.  It is expected to be particularly useful in multi-disciplinary design.</p

Visualization methodologies in aircraft design optimization

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Review of efficient surrogate infill sampling criteria with constraint handling

This paper discusses the benefits of different infill sampling criteria used in surrogate-model-based constrained global optimization. Here surrogate models are used to approximate both the objective and constraint functions with the assumption that these are computationally expensive to compute. The construction of these surrogates (also known as meta models or response surface models) involves the selection of a limited number of designs, evaluated using the original expensive functions. Conventionally this involves two stages. First the surrogate is built using an initial sampling plan; the second stage uses infill sampling criteria to select further designs that offer model improvement. This paper provides a comparison of three different infill criteria previously used in constrained global optimization problems. Particular attention is paid to the need to balance the needs of wide ranging exploration and focussed exploitation during global optimization if good results are to be achieve

Pattern search algorithm for Blackboard-based Multidisciplinary Design Optimisation frameworks

Preliminary aircraft design necessitates the use of a range of analysis tools, which are often scattered among many departments in an organisation and require regular tuning from skilled operators. For this reason, a distributed Multidisciplinary Design Optimisation approach that permits individual organisational domains to use their preferred analysis and optimisation tools would be most suitable. This paper revisits a Blackboard framework, which uses simple heuristics to automatically guide organisational design domains to a single optimum by narrowing the bounds on the shared design variables. The authors present a newly developed rule base for this legacy framework, which has been given the title “Multidisciplinary Pattern Search”. Two examples, one of which is for conceptual transonic wing design, demonstrate the merit of the newly developed rule base, database and visualisation modules. They also serve as a means for comparisons with two established Multidisciplinary Design Optimisation architectures. The results indicate that the Blackboard performs better than the distributed Collaborative Optimisation approach, albeit worse than the monolithic Simultaneous Analysis and Design method that tends to be organisationally disruptive to implemen

Data sets for the publication: &quot;A pattern search algorithm for distributed blackboard based multidisciplinary design optimisation frameworks&quot;

This dataset includes the raw data used to generate Figures 5, 7-15 in the publication &quot;A pattern search algorithm for distributed blackboard based multidisciplinary design optimisation frameworks&quot; Journal of Aircraft</span

On the coordination of multidisciplinary design optimization using expert systems

Multidisciplinary Design Optimization (MDO) of complex systems in the enterprise is typically broken down along domain specialist lines with associated expertise, tools, method and process. This paper investigates an approach to MDO that exploits heuristic control of the bounds of the common design variables across the domains of a decomposed problem. By bringing the common design variable vector to a single point in the design space, in the context of internally consistent and multiple discipline feasible state variables (and consistently resolved local design vectors), the MDO problem is solved. We present a system level management system in which an expert system is used to coordinate the activities of the domain level optimizers. Motivated by move limit and trust region algorithms a rule base has been developed to manage the bounds on the common design variable vector, control the exchange and relaxation of state coupling variables and control the specification of the domain level optimization problems. Through application of the rule base across a couple of representative MDO problems assembled from the literature the viability and performance of the method are discussed

On the coordination of multidisciplinary design optimization using expert systems

In the design of complex engineering systems involving multiple disciplines it is critical that the interactions between the subsystems of the problem are counted for. Only by considering the fully coupled system can an optimal design emerge