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

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

The quest for a truly parsimonious airfoil parameterisation scheme

The conceptual phase of the aircraft design process demands a parsimonious description of the airframe geometry. While there is no hard and fast upper limit on the affordable number of variables, the so-called 'curse of dimensionality' must always be kept in mind: if a thorough, conceptual level search of a one-variable space can be accomplished by the evaluation of n candidate designs, the same level of thoroughness (however one chooses to define this) will demand nk evaluations in k-dimensional space. Therefore, to make the design search tractable and the complexity of the geometry definition at a level where the effect of the variables can be readily understood by the designer, the number of airframe definition variables should be minimized. This has an impact on all of the components, perhaps most importantly on airfoil-type section definitions that feature on all 'wing-like' surfaces. It is therefore imperative to define these sections as parsimoniously as possible. In this paper we examine a series of parameterization schemes, whose chief conception criterion was conciseness in terms of the number of design variables. Another constraint we are considering is the ease of implementation in a commercial off-the-shelf Computer Aided Design engine

Automated optimal design of a two-stage helical gear reducer

The design space of multi-stage transmissions is usually very large and heavily constrained. This places significant demands on the algorithm employed to search it, but successful optimization has the potential to yield considerably better designs than conventional heuristics, at the same time enabling a better understanding of the trade-offs between various objectives (such as service life and overall weight). Here we tackle a two-stage helical gear transmission design problem (complete with the sizing and selection of shafts, bearings, housing, etc.) using a two-phase evolutionary algorithm in a formulation that can be extended to include additional stages or different layouts

Concise airfoil representation via case-based knowledge capture.

The cost of exploring a k-dimensional design space at a sampling density n is of the order nk. In view of this “curse of dimensionality,” the paper explores the possibility of reducing the dimensionality of parametric airfoil definitions to as low as one, to minimize their cost impact on full-airframe conceptual design studies. A formulation based on nonuniform rational B-splines is introduced in which the parametric airfoil is constructed in a reduceddimensionality space defined in terms of a small number of basis geometries. These bases are airfoils themselves, selected to represent key features of their class; we use them as learning cases or case-based representations of our knowledge of what makes a nonuniform rational B-splines curve an airfoil: moreover, an airfoil belonging to a certain class. This study focuses on supercritical sections, but the template presented here can also be applied to other types of airfoils and, indeed, to other classes of curves and surfaces

Effective geographically dispersed student teams – A teleoperated systems design case study

In the academic year 2016-17 the University of Missouri-Kansas City and the University of Southampton teamed up for a coordinated capstone design project that integrated expertise from both institutions. The design project was focused on the teleoperated deployment of atmospheric sensing equipment into localised, severe weather events. Seven aerospace engineering undergraduate students at the University of Southampton designed, fabricated, and tested a remotely-piloted aircraft that was capable of delivering atmospheric sensing packages to a target location; they also developed the telemetry-enabled weather observation platforms themselves. Simultaneously, four mechanical engineering undergraduate students from the University of Missouri developed, constructed, and tested the ground-based component of the observation system: a remotely-operated rover that could carry the aircraft and launch it from a pre-selected site in the close proximity of the targeted weather event. In April 2017 the Southampton team traveled from the United Kingdom to Kansas City, MO for a complete operational test demonstration. This paper outlines the motivation for the design activities, as well as the student efforts throughout the project, also looking at the collaborative aspects of the project and the coordination from universities more than 4,000 miles apart.</p