Stochastic level-set method for shape optimisation

We present a new method for stochastic shape optimisation of engineering structures. The method generalises an existing deterministic scheme, in which the structure is represented and evolved by a level-set method coupled with mathematical programming. The stochastic element of the algorithm is built on the methods of statistical mechanics and is designed so that the system explores a Boltzmann-Gibbs distribution of structures. In non-convex optimisation problems, the deterministic algorithm can get trapped in local optima: the stochastic generalisation enables sampling of multiple local optima, which aids the search for the globally-optimal structure. The method is demonstrated for several simple geometrical problems, and a proof-of-principle calculation is shown for a simple engineering structure.Comment: 17 pages, 10 fig

Optimising towards robust metal forming processes

Product improvement and cost saving have always been important goals in the metal forming\ud industry. Numerical optimisation can help to achieve these goals, but optimisation with a deterministic\ud approach will often lead to critical process settings, such that the slightest variation in e.g. material behaviour\ud will result in violation of constraints. To avoid a high scrap ratio, process robustness must be considered in the\ud optimisation model. Optimising for robustness includes Robust Manufacturing (RM) techniques, Optimisation\ud Under Uncertainty (OUU) methods and Finite Element (FEM) simulations of the processes. In this paper,\ud we review RM and OUU. Subsequently, the combination of Statistical Process Control (SPC), robust and\ud reliability based optimisation methods, and FEM-based process simulation implemented in AutoForm-Sigma\ud is presented. An automotive deep drawing application demonstrates the potential of strategies that optimise\ud towards robust metal forming processes

Selective maintenance optimisation for series-parallel systems alternating missions and scheduled breaks with stochastic durations

This paper deals with the selective maintenance problem for a multi-component system performing consecutive missions separated by scheduled breaks. To increase the probability of successfully completing its next mission, the system components are maintained during the break. A list of potential imperfect maintenance actions on each component, ranging from minimal repair to replacement is available. The general hybrid hazard rate approach is used to model the reliability improvement of the system components. Durations of the maintenance actions, the mission and the breaks are stochastic with known probability distributions. The resulting optimisation problem is modelled as a non-linear stochastic programme. Its objective is to determine a cost-optimal subset of maintenance actions to be performed on the components given the limited stochastic duration of the break and the minimum system reliability level required to complete the next mission. The fundamental concepts and relevant parameters of this decision-making problem are developed and discussed. Numerical experiments are provided to demonstrate the added value of solving this selective maintenance problem as a stochastic optimisation programme

A stochastic framework for multiscale strength prediction using adaptive discontinuity layout optimisation (ADLO)

The prediction of strength properties of matrix-inclusion materials, which in general are random in nature due to their spatial distribution and variation of pores, particles, and matrix-inclusion interfaces, plays an important role with regard to the reliability of materials and structures. The recently developed discontinuity layout optimisation (DLO) [18] and adaptive discontinuity layout optimisation (ADLO) [4], which can be used for determination of strength properties of materials [3, 4] and structures [9], are included in a stochastic framework, using random variables. Therefore different material properties, influencing the overall strength of the matrix-inclusion material (e.g. matrix and inclusion strength, number and distribution of pores/particles) in a considered RVE are assumed to follow certain probability distributions [12]. A sensitivity study for the identification of material parameters showing the largest influence on the strength of the considered matrix-inclusion materials is performed. The obtained results provide first insight into the nature of the reliability of strength properties of matrix-inclusion materials, paving the way to a better understanding and finally improvement of the effective strength properties of matrix-inclusion materials

The Effect of Stochastic Noise on Quantum State Transfer

We consider the effect of classical stochastic noise on control laser pulses used in a scheme for transferring quantum information between atoms, or quantum dots, in separate optical cavities via an optical connection between cavities. We develop a master equation for the dynamics of the system subject to stochastic errors in the laser pulses, and use this to evaluate the sensitivity of the transfer process to stochastic pulse shape errors for a number of different pulse shapes. We show that under certain conditions, the sensitivity of the transfer to the noise depends on the pulse shape, and develop a method for determining a pulse shape that is minimally sensitive to specific errors.Comment: 10 pages, 9 figures, to appear in Physical Review

Optimising continuous microstructures: a comparison of gradient-based and stochastic methods

This work compares the use of a deterministic gradient based search with a stochastic genetic algorithm to optimise the geometry of a space frame structure. The goal is not necessarily to find a global optimum, but instead to derive a confident approximation of fitness to be used in a second optimisation of topology. The results show that although the genetic algorithm searches the space more broadly, and this space has several global optima, gradient descent achieves similar fitnesses with equal confidence. The gradient descent algorithm is advantageous however, as it is deterministic and results in a lower computational cost

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

Cooperation of Nature and Physiologically Inspired Mechanism in Visualisation

A novel approach of integrating two swarm intelligence algorithms is considered, one simulating the behaviour of birds flocking (Particle Swarm Optimisation) and the other one (Stochastic Diffusion Search) mimics the recruitment behaviour of one species of ants – Leptothorax acervorum. This hybrid algorithm is assisted by a biological mechanism inspired by the behaviour of blood flow and cells in blood vessels, where the concept of high and low blood pressure is utilised. The performance of the nature-inspired algorithms and the biologically inspired mechanisms in the hybrid algorithm is reflected through a cooperative attempt to make a drawing on the canvas. The scientific value of the marriage between the two swarm intelligence algorithms is currently being investigated thoroughly on many benchmarks and the results reported suggest a promising prospect (al-Rifaie, Bishop & Blackwell, 2011). We also discuss whether or not the ‘art works’ generated by nature and biologically inspired algorithms can possibly be considered as ‘computationally creative’