Geometric perspectives on MDO and MDO architectures

Two main perspectives have been developed within the Multidisciplinary Design Optimization (MDO) literature for classifying and comparing MDO architectures: a numerical point of view and a formulation/data flow point of view. Although significant work has been done here, these perspectives have not provided much in the way of a priori information or predictive power about architecture performance. In this report, we outline a new perspective, called the geometric perspective, which we believe will be able to provide such predictive power. Using tools from differential geometry, we take several prominent architectures and describe mathematically how each constructs the space through which it moves. We then consider how the architecture moves through the space which it has constructed. Taken together, these investigations show how each architecture relates to the original feasible design manifold, how the architectures relate to each other, and how each architecture deals with the design coupling inherent to the original system. This in turn lays the groundwork for further theoretical comparisons between and analyses of MDO architectures and their behaviour using tools and techniques derived from differential geometry. © 2012 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

On the application of differential geometry to MDO

Multidisciplinary Design Optimization (MDO) is a methodology for optimizing large coupled systems. Over the years, a number of different MDO decomposition strategies, known as architectures, have been developed, and various pieces of analytical work have been done on MDO and its architectures. However, MDO lacks an overarching paradigm which would unify the field and promote cumulative research. In this paper, we propose a differential geometry framework as such a paradigm: Differential geometry comes with its own set of analysis tools and a long history of use in theoretical physics. We begin by outlining some of the mathematics behind differential geometry and then translate MDO into that framework. This initial work gives new tools and techniques for studying MDO and its architectures while producing a naturally arising measure of design coupling. The framework also suggests several new areas for exploration into and analysis of MDO systems. At this point, analogies with particle dynamics and systems of differential equations look particularly promising for both the wealth of extant background theory that they have and the potential predictive and evaluative power that they hold. © 2012 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

An investigation of higher-order multi-objective optimisation for 3D aerodynamic shape design

We investigate the performance of different variants of a suitably tailored Tabu Search optimisation algorithm on a higher-order design problem. We consider four objective func- tions to describe the performance of a compressor stator row, subject to a number of equality and inequality constraints. The same design problem has been previously in- vestigated through single-, bi- and three-objective optimisation studies. However, in this study we explore the capabilities of enhanced variants of our Multi-objective Tabu Search (MOTS) optimisation algorithm in the context of detailed 3D aerodynamic shape design. It is shown that with these enhancements to the local search of the MOTS algorithm we can achieve a rapid exploration of complicated design spaces, but there is a trade-off be- tween speed and the quality of the trade-off surface found. Rapidly explored design spaces reveal the extremes of the objective functions, but the compromise optimum areas are not very well explored. However, there are ways to adapt the behaviour of the optimiser and maintain both a very efficient rate of progress towards the global optimum Pareto front and a healthy number of design configurations lying on the trade-off surface and exploring the compromise optimum regions. These compromise solutions almost always represent the best qualitative balance between the objectives under consideration. Such enhancements to the effectiveness of design space exploration make engineering design optimisation with multiple objectives and robustness criteria ever more practicable and attractive for modern advanced engineering design. Finally, new research questions are addressed that highlight the trade-offs between intelligence in optimisation algorithms and acquisition of qualita- tive information through computational engineering design processes that reveal patterns and relations between design parameters and objective functions, but also speed versus optimum quality. © 2012 AIAA.

Application of the multi-objective Alliance algorithm to a benchmark aerodynamic optimization problem

This paper introduces a new version of the multiobjective Alliance Algorithm (MOAA) applied to the optimization of the NACA 0012 airfoil section, for minimization of drag and maximization of lift coefficients, based on eight section shape parameters. Two software packages are used: XFoil which evaluates each new candidate airfoil section in terms of its aerodynamic efficiency, and a Free-Form Deformation tool to manage the section geometry modifications. Two versions of the problem are formulated with different design variable bounds. The performance of this approach is compared, using two indicators and a statistical test, with that obtained using NSGA-II and multi-objective Tabu Search (MOTS) to guide the optimization. The results show that the MOAA outperforms MOTS and obtains comparable results with NSGA-II on the first problem, while in the other case NSGA-II is not able to find feasible solutions and the MOAA is able to outperform MOTS. © 2013 IEEE.

Testing of the multi-objective alliance algorithm on benchmark functions

A new version of the Multi-objective Alliance Algorithm (MOAA) is described. The MOAA's performance is compared with that of NSGA-II using the epsilon and hypervolume indicators to evaluate the results. The benchmark functions chosen for the comparison are from the ZDT and DTLZ families and the main classical multi-objective (MO) problems. The results show that the new MOAA version is able to outperform NSGA-II on almost all the problems.

The closed thorium-transuranic fuel cycle in reduced-moderation PWRs and BWRs

Multiple recycle of long-lived actinides has the potential to greatly reduce the required storage time for spent nuclear fuel or high level nuclear waste. This is generally thought to require fast reactors as most transuranic (TRU) isotopes have low fission probabilities in thermal reactors. Reduced-moderation LWRs are a potential alternative to fast reactors with reduced time to deployment as they are based on commercially mature LWR technology. Thorium (Th) fuel is neutronically advantageous for TRU multiple recycle in LWRs due to a large improvement in the void coefficient. If Th fuel is used in reduced-moderation LWRs, it appears neutronically feasible to achieve full actinide recycle while burning an external supply of TRU, with related potential improvements in waste management and fuel utilization. In this paper, the fuel cycle of TRU-bearing Th fuel is analysed for reduced-moderation PWRs and BWRs (RMPWRs and RBWRs). RMPWRs have the advantage of relatively rapid implementation and intrinsically low conversion ratios, which is desirable to maximize the TRU burning rate. However, it is challenging to simultaneously satisfy operational and fuel cycle constraints. An RBWR may potentially take longer to implement than an RMPWR due to more extensive changes from current BWR technology. However, the harder neutron spectrum can lead to favourable fuel cycle performance. A two-stage TRU burning cycle, where the first stage is Th-Pu MOX in a conventional PWR feeding a second stage continuous burn in RMPWR or RBWR, is technically reasonable, although it is more suitable for the RBWR implementation. In this case, the fuel cycle performance is relatively insensitive to the discharge burn-up of the first stage. © 2013 Elsevier Ltd. All rights reserved.

Thorium energy futures

The potential for thorium as an alternative or supplement to uranium in fission power generation has long been recognised, and several reactors, of various types, have already operated using thorium-based fuels. Accelerator Driven Subcritical (ADS) systems have benefits and drawbacks when compared to conventional critical thorium reactors, for both solid and molten salt fuels. None of the four options - liquid or solid, with or without an accelerator - can yet be rated as better or worse than the other three, given today's knowledge. We outline the research that will be necessary to lead to an informed choice. Copyright © 2012 by IEEE.

The production of radionuclides for nuclear medicine from a compact, low-energy accelerator system.

The field of nuclear medicine is reliant on radionuclides for medical imaging procedures and radioimmunotherapy (RIT). The recent shut-downs of key radionuclide producers have highlighted the fragility of the current radionuclide supply network, however. To ensure that nuclear medicine can continue to grow, adding new diagnostic and therapy options to healthcare, novel and reliable production methods are required. Siemens are developing a low-energy, high-current - up to 10MeV and 1mA respectively - accelerator. The capability of this low-cost, compact system for radionuclide production, for use in nuclear medicine procedures, has been considered.

Multispacecraft refueling optimization considering the J2 perturbation and window constraints

The optimization of a near-circular low-Earth-orbit multispacecraft refueling problem is studied. The refueling sequence, service time, and orbital transfer time are used as design variables, whereas the mean mission completion time and mean propellant consumed by orbital maneuvers are used as design objectives. The J2 term of the Earth's nonspherical gravity perturbation and the constraints of rendezvous time windows are taken into account. A hybridencoding genetic algorithm, which uses normal fitness assignment to find the minimum mean propellant-cost solution and fitness assignment based on the concept of Pareto-optimality to find multi-objective optimal solutions, is presented. The proposed approach is demonstrated for a typical multispacecraft refueling problem. The results show that the proposed approach is effective, and that the J2 perturbation and the time-window constraints have considerable influences on the optimization results. For the problems in which the J2 perturbation is not accounted for, the optimal refueling order can be simply determined as a sequential order or as the order only based on orbitalplane differences. In contrast, for the problems that do consider the J2 perturbation, the optimal solutions obtained have a variety of refueling orders and use the drift of nodes effectively to reduce the propellant cost for eliminating orbital-plane differences. © 2013 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

Optimization algorithms and ODE's in MDO

There is a need for a stronger theoretical understanding of Multidisciplinary Design Optimization (MDO) within the field. Having developed a differential geometry framework in response to this need, we consider how standard optimization algorithms can be modeled using systems of ordinary differential equations (ODEs) while also reviewing optimization algorithms which have been derived from ODE solution methods. We then use some of the framework's tools to show how our resultant systems of ODEs can be analyzed and their behaviour quantitatively evaluated. In doing so, we demonstrate the power and scope of our differential geometry framework, we provide new tools for analyzing MDO systems and their behaviour, and we suggest hitherto neglected optimization methods which may prove particularly useful within the MDO context. Copyright © 2013 by ASME.

Diurnal changes of behavior and respiration of Yangtze finless porpoises (Neophocaena phocaenoides asiaeorientalis) in captivity

A preliminary study was carried out to investigate diurnal changes of behavior of three, one adult mate, one adult female, and one juvenile female, Yangtze finless porpoises (Neophocaena phocaenoides asiaeorientalis) in captivity. The respiration and behavior of the porpoises were recorded for 222 hr across 42 days. Behavioral data were recorded for eight general categories: aerial display and fast swimming, begging for fish, playing, nonsexual socializing, sexual behavior, resting, rubbing, and miscellaneous (i.e., other behaviors not included in the above categories). Each behavioral category was scored using one-zero sampling with 10-min intervals. The adult male showed shorter mean respiratory intervals at night (19:00-7:00 h), whereas the mean respiratory intervals of the females were shorter during the day (7:00-19:00 h). Begging for fish of all individuals, playing of the juvenile female, nonsexual socializing, and miscellaneous behavior of the adult female and resting of the male were observed more easily in the day, and aerial display and fast swimming of the adults and resting of the females were observed more easily at night. No significant diurnal difference was found, however, in the remaining categories of each individual. Each of the three porpoises therefore showed a distinct diurnal pattern, but none was obviously more active in the daytime than during the nighttime. Results suggest that daytime-only feeding schedules may be insufficient to meet the energetic needs of marine mammals that show a 24-hr activity cycle, and that nighttime feeding may be a worthwhile addition to husbandry routines.