State-of-the-art in aerodynamic shape optimisation methods

Aerodynamic optimisation has become an indispensable component for any aerodynamic design over the past 60 years, with applications to aircraft, cars, trains, bridges, wind turbines, internal pipe flows, and cavities, among others, and is thus relevant in many facets of technology. With advancements in computational power, automated design optimisation procedures have become more competent, however, there is an ambiguity and bias throughout the literature with regards to relative performance of optimisation architectures and employed algorithms. This paper provides a well-balanced critical review of the dominant optimisation approaches that have been integrated with aerodynamic theory for the purpose of shape optimisation. A total of 229 papers, published in more than 120 journals and conference proceedings, have been classified into 6 different optimisation algorithm approaches. The material cited includes some of the most well-established authors and publications in the field of aerodynamic optimisation. This paper aims to eliminate bias toward certain algorithms by analysing the limitations, drawbacks, and the benefits of the most utilised optimisation approaches. This review provides comprehensive but straightforward insight for non-specialists and reference detailing the current state for specialist practitioners

Dynamic sampling schemes for optimal noise learning under multiple nonsmooth constraints

We consider the bilevel optimisation approach proposed by De Los Reyes, Sch\"onlieb (2013) for learning the optimal parameters in a Total Variation (TV) denoising model featuring for multiple noise distributions. In applications, the use of databases (dictionaries) allows an accurate estimation of the parameters, but reflects in high computational costs due to the size of the databases and to the nonsmooth nature of the PDE constraints. To overcome this computational barrier we propose an optimisation algorithm that by sampling dynamically from the set of constraints and using a quasi-Newton method, solves the problem accurately and in an efficient way

Protecting valuable resources using optimal control theory and feedback strategies for plant disease management

Mathematical models of tree diseases often have little to say about how to manage established epidemics. Models often show that it is too late for successful disease eradication, but few study what management could still be beneficial. This study focusses on finding effective control strategies for managing sudden oak death, a tree disease caused by Phytophthora ramorum. Sudden oak death is a devastating disease spreading through forests in California and southwestern Oregon. The disease is well established and eradication is no longer possible. The ongoing spread of sudden oak death is threatening high value tree resources, including national parks, and culturally and ecologically important species like tanoak. In this thesis we show how the allocation of limited resources for controlling sudden oak death can be optimised to protect these valuable trees. We use simple, approximate models of sudden oak death dynamics, to which we apply the mathematical framework of optimal control theory. Applying the optimised controls from the approximate model to a complex, spatial simulation model, we demonstrate that the framework finds effective strategies for protecting tanoak, whilst also conserving biodiversity. When applied to the problem of protecting Redwood National Park, which is under threat from a nearby outbreak of sudden oak death, the framework finds spatial strategies that balance protective barriers with control at the epidemic wavefront. Because of the number of variables in the system, computational and numerical limitations restrict the control optimisation to relatively simple approximate models. We show how a lack of accuracy in the approximate model can be accounted for by using model predictive control, from control systems engineering: an approach coupling feedback with optimal control theory. Continued surveillance of the complex system, and re-optimisation of the control strategy, ensures that the result remains close to optimal, and leads to highly effective disease management. In this thesis we show how the machinery of optimal control theory can inform plant disease management, protecting valuable resources from sudden oak death. Incorporating feedback into the application of the resulting strategies ensures control remains effective over long timescales, and is robust to uncertainties and stochasticity in the system. Local management of sudden oak death is still possible, and our results show how this can be achieved

Optimization of surface textures in hydrodynamic lubrication through the adjoint method

In this work we assess the applicability of the adjoint optimization technique for determining optimal surface topographies of two surfaces in relative motion in presence of a thin lubricant films that can cavitate. Among the existing numerical tools for topology optimization in engineering problems, the adjoint method represents a promising and versatile technique, which can also be applied to the field of full film tribology. In particular, the design of surfaces with complex textures can thoroughly benefit from this method, as it allows dealing with a large number of degrees of freedom at low computational cost. We show that this optimization method can be successfully applied to cavitating lubricant flows such as in pin-on-disc tribometers, giving the possibility to extend the results also to other typical applications such as journal and slider bearings. It is shown that the adjoint method can optimize the whole gap height distribution point by point in a more efficient way than traditional optimization approaches and parametric studies. In particular, thanks to the sensitivity analysis the adjoint method is able to find the placement and depth profile of each texture element

Optimal Control of Convective FitzHugh-Nagumo Equation

We investigate smooth and sparse optimal control problems for convective FitzHugh-Nagumo equation with travelling wave solutions in moving excitable media. The cost function includes distributed space-time and terminal observations or targets. The state and adjoint equations are discretized in space by symmetric interior point Galerkin (SIPG) method and by backward Euler method in time. Several numerical results are presented for the control of the travelling waves. We also show numerically the validity of the second order optimality conditions for the local solutions of the sparse optimal control problem for vanishing Tikhonov regularization parameter. Further, we estimate the distance between the discrete control and associated local optima numerically by the help of the perturbation method and the smallest eigenvalue of the reduced Hessian

Designing manufacturable viscoelastic devices using a topology optimization approach within a truly-mixed fem framework

A new approach to topology optimization is presented that is based on the minimization of the input/output transfer function H∞norm. Additionally, by properly selecting input and output vector, the approach is recognized to minimize an entirely new definition of frequency-based dynamic compliance. The method is applied to viscoelastic systems in plane strain conditions that are investigated by using the Arnold-Winther finite-element resorting to a generalized solid phenomenological model. Preliminary indications on how to address the actual manufacturability of the optimal specimen are eventually outlined

A study of the application of singular perturbation theory

A hierarchical real time algorithm for optimal three dimensional control of aircraft is described. Systematic methods are developed for real time computation of nonlinear feedback controls by means of singular perturbation theory. The results are applied to a six state, three control variable, point mass model of an F-4 aircraft. Nonlinear feedback laws are presented for computing the optimal control of throttle, bank angle, and angle of attack. Real Time capability is assessed on a TI 9900 microcomputer. The breakdown of the singular perturbation approximation near the terminal point is examined Continuation methods are examined to obtain exact optimal trajectories starting from the singular perturbation solutions