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We consider a deformation
of the Dedekind eta function depending on two
-dimensional simple lattices
and two parameters
$(m,t)\in (0,\infty )$
, initially proposed by Terry Gannon. We show that the minimisers of the lattice theta function are the maximisers of
in the space of lattices with fixed density. The proof is based on the study of a lattice generalisation of the logarithm, called the lattice logarithm, also defined by Terry Gannon. We also prove that the natural logarithm is characterised by a variational problem over a class of one-dimensional lattice logarithms.
In this paper, a rectangular aerostatic bearing with multiple supply holes is optimised with a multiobjective optimisation approach. The design variables taken into account are the supply holes position, their number and diameter, the supply pressure, while the objective functions are the load capacity, the air consumption and the stiffness and damping coefficients. A genetic algorithm is applied in order to find the Pareto set of solutions. The novelty with respect to other optimisations which can be found in literature is that number and location of the supply holes is completely free and not associated to a pre-defined scheme. A vector x associated with the supply holes location is introduced in the design parameters and given in input to the optimizer.
The computer aided internal optimisation (CAIO) method produces an optimised fibre layout for parts made from fibre-reinforced plastics (FRP), starting from an initial shell geometry and a given load case. Its main principle is iterative reduction of shear stresses by aligning fibre main axes with principal normal stress trajectories. Previous contributions, ranging from CAIO’s introduction over testing to extensions towards multi-layer FRP laminates, highlighted its lightweight design potential. For its application to laminate design approaches, alterations have been proposed; however, questions remain open. These questions include which convergence criteria to use, how to handle ambiguous principle normal stress trajectories, influence of using multi-layer CAIO optimisation instead of the initial single-layer CAIO and how dire consequences of slightly deviating fibre orientations from the optimised trajectories are. These challenges are discussed in depth and guidelines are given. This paper is an enhanced version of a distinguished contribution at the first symposium ‘Lightweight Design in Product Development’, Zurich (June 14–15, 2018).
This paper attempts to solve a challenge in online relative optimal path planning of unmanned surface vehicles (USVs) caused by current and wave disturbance in the practical marine environment. The asymptotically optimal rapidly extending random tree (RRT*) method for local path optimisation is improved. Based on that, an online path planning (OPP) scheme is proposed according to the USV's kinematic and dynamic model. The execution efficiency of RRT* is improved by reduction of the sampling space that is used for randomly learning environmental knowledge. A heuristic sampling scheme is proposed based on the proportional navigation guidance (PNG) method that is used to enable the OPP procedure to utilise the reference information of the global path. Meanwhile, PNG is used to guide RRT* in generating feasible paths with a small amount of gentle turns. The dynamic obstacle avoidance problem is also investigated based on the International Regulations for Preventing Collisions at Sea. Case studies demonstrate that the proposed method efficiently plans paths that are relatively easier to execute and lower in fuel expenditure than traditional schemes. The dynamic obstacle avoidance ability of the proposed scheme is also attested.
Exergy efficiency can be used as an objective function in order to improve systems efficiency. Thus, the most efficient regions for the operation parameters can be searched easily. Exergy efficiency data of a turboprop engine’s components that have been calculated using basic engine parameters in the previous studies are modeled using cubic spline curve fitting methodology. Spline curves are on the two dimensional plane, where x axis is the input parameter and y axis is the exergy efficiency of the component. A spline curve is defined by the points subject to arbitrary selection of number and position. Initially positions of the points are located with two different methods and then in order to obtain better accuracy point positions are improved by ‘Ant colony’ and ‘Goldsection’ optimisation methods. Sum of Squares of the errors between the fitted value and data value was used as the fitness function. Least square error of 5 × 10−9 is assumed as acceptable accuracy which yields to a minimum R = 0.9998 linear correlation coefficient. In the optimisation step, independent engine variable versus calculated engine performance parameters were checked against spline fitted values. Improvement of the fitness function is observed as the number of fitting points is increased. Ant colony optimisation in engine exergy efficiency parametric modeling is a new approach in authors’ point of view.
There is an emerging body of legal thought directed at contemporary profiling and data science. Some of this focuses on limiting ‘human computability’, some addresses questions of ‘manipulation’ and ‘behavioural optimisation’, and some suggests ways to introduce friction into the information environment to interrupt the translation of data into meaning. This chapter looks at how some of these ideas might be implemented as computational legal applications. It argues that the legal subject of algorithmic accountability can be expanded into a rights-bearing entity that can actively contest how it is computationally interpreted, through mechanisms of ‘contestation by design’. The chapter also describes the utility of concepts like ‘context’ for building boundaries and friction into information architectures, not simply in terms of information flow but also for constraining how the design of those architectures influences and structures behaviour. Finally, it suggests the shape of a new ‘composite’ legal person as a mechanism to constrain profiling behavior by producing an identity as an interface to the ‘world state’ it inhabits.
This paper evaluates six supersonic business jet (SSBJ) concepts in a multidisciplinary design analysis optimisation (MDAO) environment in terms of their aerodynamics and sonic boom intensities. The aerodynamic analysis and sonic boom prediction are investigated by a number of conceptual-level numerical approaches. The panel method PANAIR is integrated to perform automated aerodynamic analysis. The drag coefficient is corrected by the Harris wave drag formula and form factor method. For sonic boom prediction, the near-field pressure is predicted through the Whitham F-function method. The F-function is decomposed to the F-function due to volume and the F-function due to lift to investigate the separate effect on sonic boom. The propagation method for the near-field signature in a stratified windy atmosphere is the waveform parameter method. In this research, using the methods described and publically available data on the concepts, the supersonic drag elements and sonic boom signature due to volume distribution and lift distribution are analysed. Based on the analysis, low-boom and low-drag design principles are identified.
The paper presents the design and experimental testing of the control system used in a new morphing wing application with a full-scaled portion of a real wing. The morphing actuation system uses four similar miniature brushless DC (BLDC) motors placed inside the wing, which execute a direct actuation of the flexible upper surface of the wing made from composite materials. The control system of each actuator uses three control loops (current, speed and position) characterised by five control gains. To tune the control gains, the Particle Swarm Optimisation (PSO) method is used. The application of the PSO method supposed the development of a MATLAB/Simulink® software model for the controlled actuator, which worked together with a software sub-routine implementing the PSO algorithm to find the best values for the five control gains that minimise the cost function. Once the best values of the control gains are established, the software model of the controlled actuator is numerically simulated in order to evaluate the quality of the obtained control system. Finally, the designed control system is experimentally validated in bench tests and wind-tunnel tests for all four miniature actuators integrated in the morphing wing experimental model. The wind-tunnel testing treats the system as a whole and includes, besides the evaluation of the controlled actuation system, the testing of the integrated morphing wing experimental model and the evaluation of the aerodynamic benefits brought by the morphing technology on this project. From this last perspective, the airflow on the morphing upper surface of the experimental model is monitored by using various techniques based on pressure data collection with Kulite pressure sensors or on infrared thermography camera visualisations.
We examined the feasibility of linear programming (LP) to develop diets that were economical, included traditional (cultural, non-market) foods and met the dietary reference intakes (DRI) in a Canadian Indigenous population. Diet optimisation using LP is a mathematical technique that can develop food-based dietary guidelines for healthy eating in Indigenous populations where food insecurity, availability and cost are important considerations. It is a means of developing nutritionally optimal food combinations that are based on economical and culture-specific foods. Observed food consumption data were derived using 24-h food recalls from the First Nations Food, Nutrition and Environment Study. The LP models were constructed to develop diets meeting DRI, cost and food constraints. Achieving the recommended food intake was not feasible in a model meeting all nutrient requirements. Models that met most nutrient requirements at reduced cost were designed for men and women, separately. In women, it was necessary to increase energy intake to meet most nutrient requirements. Nutrient requirements could not be met for fibre, linoleic and linolenic acids, vitamin D, Ca and K in both sexes, P in women, and Mg and vitamin A in men. Using LP to develop optimal diets for First Nations people, we found simultaneous achievement of all DRI was difficult, suggesting that supplementation might be necessary which goes against recommendations for individuals to meet their nutrient needs through healthy eating patterns. Additionally, to make diets feasible, programmes to reduce market food costs and to support First Nations people in traditional food harvesting are recommended.
Navigation methods, traditional and modern, use lines of position in the plane. Standard Gaussian assumptions about errors leads to a constant sum of squared distances from the lines defining a probability contour. It is well known these contours are a family of ellipses centred on the most probable position and they can be computed using algebraic methods. In this paper we show how the most probable position, the axes and foci of ellipses can be found using geometric methods. This results in a ruler and compasses construction of these points and this gives insight into the way the shape and orientation of the probability contours depend on the angles between the lines of position. We start with the classical case of three lines of position with equal variances, we show how this can be extended to the case where the variances in the errors in the lines of position differ, and we go on to consider the case of four lines of position using a methodology that generalises to an arbitrary number of lines.
The maximum attainable performance of small gas turbines represents a strong limitation to the operating altitude and endurance of high-altitude unmanned aerial vehicles (UAVs). Significant improvement of the cycle thermal efficiency can be achieved through the introduction of heat exchangers, with the consequent increase of the overall engine weight. Since semi-closed cycle engines can achieve a superior degree of compactness compared to their open cycle counterparts, their use can offset the additional weight of the heat exchangers. This paper applies semi-closed cycles to a high-altitude UAV propulsion system, with the objective of assessing the benefits introduced on the engine performance and weight. A detailed model has been created to account for component performance and size variation as function of thermodynamic parameters. The sizing has been coupled with a multi-objective optimisation algorithm for minimum specific fuel consumption and weight. Results of two different semi-closed cycle configurations are compared with equivalent state-of-the-art open cycles, represented by a recuperated and an intercooled-recuperated engine. The results show that, for a fixed design power output, engine weight is approximately halved compared to state-of-the-art open cycles, with slightly improved specific fuel consumption performance. Optimum semi-closed cycles furthermore operate at higher overall pressure ratios than open cycles and make use of recuperators with higher effectiveness as the mass penalty of the recuperator is smaller due to the lower engine mass flow rates.
A growing interest in constellations of small satellites has recently emerged due to the increasing capability of these platforms and their reduced time and cost of development. However, in the absence of dedicated launch services for these systems, alternative methods for the deployment of these constellations must be considered which can take advantage of the availability of secondary-payload launch opportunities. Furthermore, a means of exploring the effects and tradeoffs in corresponding system architectures is required. This paper presents a methodology to integrate the deployment of constellations of small satellites into the wider design process for these systems. Using a method of design-space exploration, enhanced understanding of the tradespace is supported , whilst identification of system designs for development is enabled by the application of an optimisation process. To demonstrate the method, a simplified analysis framework and a multiobjective genetic algorithm are implemented for three mission case-studies with differing application. The first two cases, modelled on existing constellations, indicate the benefits of design-space exploration, and possible savings which could be made in cost, system mass, or deployment time. The third case, based on a proposed Earth observation nanosatellite constellation, focuses on deployment following launch using a secondary-payload opportunity and demonstrates the breadth of feasible solutions which may not be considered if only point-designs are generated by a priori analysis. These results indicate that the presented method can support the development of future constellations of small satellites by improving the knowledge of different deployment strategies available during the early design phases and through enhanced exploration and identification of promising design alternatives.
The maximisation of control power is considered for an aircraft with multiple control surfaces, with the force and moment coefficients specified by polynomials of the control surface deflections of degree two. The optimal deflections, which maximise and minimise any force or moment coefficient, are determined subject to constraints on the range of deflection of each control surface. The results are applied to a flying wing configuration to determine: (i/ii) the pitch trim, at the lowest drag for the fastest climb, and at the highest drag for the steepest descent; (iii) the maximum and minimum pitching moment; (iv) the maximum and minimum yaw control power and the fraction needed to compensate an outboard engine failure for several propulsion configurations; (v) the maximum and minimum rolling moment. The optimal use of all control surfaces has significant advantages over using just one, e.g. the range of drag modulation with pitch trim is much wider and the maximum and minimum available control moments larger.
To derive healthy and sustainable food-based dietary guidelines (FBDG) for different target groups in the Netherlands and describe the process.
Optimised dietary patterns for children, adolescents, adults and the elderly were calculated using an optimisation model. Foods high in saturated and trans-fatty acids, salt and sugar, and low in dietary fibre, were excluded. The dietary patterns resembled the current food consumption as closely as possible, while simultaneously meeting recommendations for food groups, nutrients, maximum limits for foods with a high environmental impact, and within 85 % of the energy requirement. Recommended daily amounts of food groups were based on the optimised dietary patterns and expert judgement.
FBDG were derived for Dutch people with different ages, genders, activity levels and food preferences.
For most target groups the optimisation model provided dietary patterns that complied with all requirements. For some food groups, the optimised amounts varied largely between target groups. For consistent messages to consumers, the optimised dietary patterns were adjusted to uniform recommendations per target group. Recommendations were visualised in the Wheel of Five. The advice is to eat the recommended amounts of foods according to the Wheel of Five and limit consumption of other foods.
Based on an optimisation model, scientific evidence, information on dietary patterns and expert knowledge, we derived FBDG for different target groups. The Wheel of Five is a key food-counselling model that can help Dutch consumers to make their diets healthier and more environmentally sustainable.
To maintain functional tolerances of gear sets over their lifetime, especially in polymer-seel gear sets, the wear behaviour must be considered. The state of the art in wear modelling does not take the run-in behaviour of polymer-metal contacts into account. This results in oversizing of wear allowances in the stationary wear phase and undersizing in the run-in phase. Therefore, a modified wear model is presented in this paper. With this method the issues of over- and undersizing can be eliminated.
The method is then applied in a case study to show two things. Firstly, using the presented method the calculated necessary wear allowances were reduced by 30%. Secondly, the effect of surface structures on the wear behaviour was investigated. It is shown that the run-in process is not dependent on roughness in sliding direction, but on overall contact area. Thus, the state of the art, i.e. tolerating only the roughness in sliding direction, is insufficient. Considering the process-induced surface topology during design of gear sets can decrease run-in wear. Together with the optimised wear model, this allows wider manufacturing tolerances and thus lower costs during production.
It is generally accepted in industry and academia that trade-offs between functional design objectives are an inevitable factor in the development of mechanical systems. These trade-offs can have a large influence on the achievable robustness and performance of the final design, with many products only functioning in narrow sweet-spots between different objectives. As a result, the design process of multi- functional products can be prolonged when designers concurrently attempt to find sweet-spots between a number of potentially interdependent trade-offs. This paper will show that designers only have six different approaches available when attempting to manage a trade-off while trying to ensure robustness and a sufficient performance. These fall within one of three categories; accept, optimise, or redesign. Selecting the wrong approach, can result in consequences downstream which can be difficult to predict, amongst others a lack of robustness to geometric variation, constrained performance, and long development lead time. This points to a substantial potential in the synthesis of design methods that support the identification and management of trade-offs in early product development.
Electric Vehicles (EVs) are very quite at low speed, which can be hazardous for pedestrians. It is necessary to add warning sounds but this can represent an annoyance if they are poorly designed. On the other hand, they can be not enough detectable because of the masking effect due to the background noise. In this paper, we propose a method for the design of EV sounds that takes into account in the same time detectability and unpleasantness. It is based on user tests and implements Interactive Genetic Algorithms (IGA) for the optimization of the sounds. Synthesized EV sounds, based on additive synthesis and filtering, are proposed to a set of participants during a hearing test. An experimental protocol is proposed for the assessment of the detectability and the unpleasantness of the EV sounds. After the convergence of the method, sounds obtained with the IGA are compared to different sound design proposals. Results show that the quality of the sounds designed by the IGA method is significantly higher than the design proposals, validating the relevance of the approach.
The Life Cycle Energy Optimisation (LCEO) methodology aims at finding a design solution that uses a minimum amount of cumulative energy demand over the different phases of the vehicle's life cycle, while complying with a set of functional constraints. This effectively balances trade-offs, and therewith avoids sub-optimal shifting between the energy demand for the cradle-to-production of materials, operation of the vehicle, and end-of-life phases. The present work describes the extension of the LCEO methodology to perform holistic product system optimisation. The constrained design of an automotive component and the design of a subset of the processes which are applied to it during its life cycle are simultaneously optimised to achieve a minimal product system life cycle energy. A subset of the processes of the end-of-life phase of a vehicle's roof are modeled through a continuous formulation. The roof is modeled as a sandwich structure with its design variables being the material compositions and the thicknesses of the different layers. The results show the applicability of the LCEO methodology to product system design and the use of penalization to ensure solution feasibility.