Multi-fidelity optimization via surrogate modelling

This paper demonstrates the application of correlated Gaussian process based approximations to optimization where multiple levels of analysis are available, using an extension to the geostatistical method of co-kriging. An exchange algorithm is used to choose which points of the search space to sample within each level of analysis. The derivation of the co-kriging equations is presented in an intuitive manner, along with a new variance estimator to account for varying degrees of computational ‘noise’ in the multiple levels of analysis. A multi-fidelity wing optimization is used to demonstrate the methodology

A geometry optimization framework for photonic crystal design

AbstractThe performance of photonic crystal devices can depend strongly on their geometry. Alas, their fundamental physics offers relatively little by way of pointers in terms of optimum shapes, so numerical design search techniques must be used in an attempt to determine high performance layouts. We discuss strategies for solving this type of optimization problem, the main challenge of which is the conflict between the enormous size of the space of potentially useful designs and the relatively high computational cost of evaluating the performance of putative shapes. The optimization technique proposed here operates over increasing levels of fidelity, both in terms of the resolution of its non-parametric shape definition and in terms of the resolution of the numerical analysis of the performance of putative designs. This is a generic method, potentially applicable to any type of electromagnetic device shape design problem. We also consider a methodology for assessing the robustness of the optima generated through this process, investigating the impact of manufacturing errors on their performance. As an illustration, we apply this technology to the design of a two-dimensional photonic crystal structure; the result features a large complete band gap structure and a topology that is different from previously published designs

Building a traceable climate model hierarchy with multi-level emulators

To study climate change on multi-millennial timescales or to explore a model’s parameter space, efficient models with simplified and parameterised processes are required. However, the reduction in explicitly modelled processes can lead to underestimation of some atmospheric responses that are essential to the understanding of the climate system. While more complex general circulations are available and capable of simulating a more realistic climate, they are too computationally intensive for these purposes. In this work, we propose a multi-level Gaussian emulation technique to efficiently estimate the outputs of steady-state simulations of an expensive atmospheric model in response to changes in boundary forcing. The link between a computationally expensive atmospheric model, PLASIM (Planet Simulator), and a cheaper model, EMBM (energy–moisture balance model), is established through the common boundary condition specified by an ocean model, allowing for information to be propagated from one to the other. This technique allows PLASIM emulators to be built at a low cost. The method is first demonstrated by emulating a scalar summary quantity, the global mean surface air temperature. It is then employed to emulate the dimensionally reduced 2-D surface air temperature field. Even though the two atmospheric models chosen are structurally unrelated, Gaussian process emulators of PLASIM atmospheric variables are successfully constructed using EMBM as a fast approximation. With the extra information gained from the cheap model, the multi-level emulator of PLASIM’s 2-D surface air temperature field is built using only one-third the amount of expensive data required by the normal single-level technique. The constructed emulator is shown to capture 93.2% of the variance across the validation ensemble, with the averaged RMSE of 1.33 °C. Using the method proposed, quantities from PLASIM can be constructed and used to study the effects introduced by PLASIM’s atmosphere

An activity-based-parametric hybrid cost model to estimate the unit cost of a novel gas turbine component

The first tool presented in this paper is a generic factory cost model that can estimate various costs at multiple levels of any manufacturing plant. The model is activity based which means that the cost of each manufacturing operation is calculated and then summed up so that the true £-per-hour factory cost rate as well as the exact unit cost (i.e. manufacturing cost) of an unlimited number of different components can be estimated.The second tool is a scalable cost model that predicts the unit cost of future integrally bladed disc (blisk) designs that are found in gas turbine compressors. The tool multiplies the machine cost rates, calculated by the factory cost model, by the operation times derived from blisk scaling rules. As the operation times often depend on the number of blades, the disc diameter and other design variables, many scaling rules are based on the correlation between operation times and certain design parameters. Conversely, the remaining process times are constant because they are independent of the blisk geometry. As future process times can only be estimated and the correlation between operation times and design parameters is never perfect, all operation times have uncertainty distributions. These are cascaded through the model to generate a probability distribution of the unit cost.Through the interactive exchange of detailed cost information at the manufacturing operation level as well as extrapolated operation times, the two cost models facilitate design and manufacturing engineering to concurrently optimise blisk designs and manufacturing processes in terms of cost

Tradeoffs in jet inlet design: a historical perspective

The design of the inlet(s) is one of the most demanding tasks of the development process of any gas turbine-powered aircraft. This is mainly due to the multi-objective and multidisciplinary nature of the exercise. The solution is generally a compromise between a number of conflicting goals and these conflicts are the subject of the present paper. We look into how these design tradeoffs have been reflected in the actual inlet designs over the years and how the emphasis has shifted from one driver to another. We also review some of the relevant developments of the jet age in aerodynamics and design and manufacturing technology and we examine how they have influenced and informed inlet design decision