Design space reduction in optimization using generative topographic mapping

Dimension reduction in design optimization is an extensively researched area. The need arises in design problems dealing with very high dimensions, which increase the computational burden of the design process because the sample space required for the design search varies exponentially with the dimensions. This work describes the application of a latent variable method called Generative Topographic Mapping (GTM) in dimension reduction of a data set by transformation into a low-dimensional latent space. The attraction it presents is that the variables are not removed, but only transformed and hence there is no risk of missing out on information relating to all the variables. The method has been tested on the Branin test function initially and then on an aircraft wing weight problem. Ongoing work involves finding a suitable update strategy for adding infill points to the trained GTM in order to converge to the global optimum effectively. Three update methods tested on GTM so far are discussed

An adjoint for likelihood maximization

The process of likelihood maximization can be found in many different areas of computational modelling. However, the construction of such models via likelihood maximization requires the solution of a difficult multi-modal optimization problem involving an expensive O(n3) factorization. The optimization techniques used to solve this problem may require many such factorizations and can result in a significant bottle-neck. This article derives an adjoint formulation of the likelihood employed in the construction of a kriging model via reverse algorithmic differentiation. This adjoint is found to calculate the likelihood and all of its derivatives more efficiently than the standard analytical method and can therefore be utilised within a simple local search or within a hybrid global optimization to accelerate convergence and therefore reduce the cost of the likelihood optimization

Capture of manufacturing uncertainty in turbine blades through probabilistic techniques

Efficient designing of the turbine blades is critical to the performance of an aircraft engine. An area of significant research interest is the capture of manufacturing uncertainty in the shapes of these turbine blades. The available data used for estimation of this manufacturing uncertainty inevitably contains the effects of measurement error/noise. In the present work, we propose the application of Principal Component Analysis (PCA) for de-noising the measurement data and quantifying the underlying manufacturing uncertainty. Once the PCA is performed, a method for dimensionality reduction has been proposed which utilizes prior information available on the variance of measurement error for different measurement types. Numerical studies indicate that approximately 82% of the variation in the measurements from their design values is accounted for by the manufacturing uncertainty, while the remaining 18% variation is filtered out as measurement error

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

Closing the communications loop on the computerized peer‐assessment of essays

The use of self‐ and peer‐assessment is not new to higher education. Traditionally its use has required the complex and time‐consuming management of coursework submissions by the tutor, in an attempt to maintain validity and anonymity of the assessment process. In the last few years a number of computerized systems have been developed that are capable of automatically supporting, managing and performing the assessment process. The requirement for student anonymity and the release of the tutor from the process of marking have reduced the ability to develop the iterative process of feedback. This feedback is considered essential in supporting student learning and developing reflective practice. This paper describes the enhancement of a computerized assessment system to support anonymous computer‐mediated discussion between marker and marked having previously performed peer‐assessment. A detailed description is provided of the integrated assessment process, and an analysis of the use of this anonymous discussion is presented. Anonymous student feedback is presented and analyzed with respect to the perceived benefits of using the system with respect to enhancing the student learning process

Improving the optimisation performance of an ensemble of radial basis functions

In this paper we investigate surrogate-based optimisation performance using two different ensemble approaches, and a novel update strategy based on the local Pearson correlation coefficient. The ?first ensemble, is based on a selective approach, where ns RBFs are constructed and the most accurate RBF is selected for prediction at each iteration, while the others are ignored. The secondensemble uses a combined approach, which takes advantage of ns different RBFs, in the hope of reducing errors in the prediction through a weighted combination of the RBFs used. The update strategy uses the local Pearson correlation coefficient as a constraint to ignore domain areas wherethere is disagreement between the surrogates. In total the performance of six different approaches are investigated, using ?five analytical test functions with 2 to 50 dimensions, and one engineering problem related to the frequency response of a satellite boom with 2 to 40 dimensions

Grid-enabled electromagnetic optimisation (GEM) for industrial use.

We have developed a tool for parametric electromagnetic design studies using industrial analysis code for the design search and optimisation of photonic crystals. This software tool allows engineering users to transparently access Grid compute components for an end-to-end design of a photonic device using computational electromagnetics. In this paper, we give an overview of the industrial application background, present some aspects of the interface developed, and discuss some of the issues involved in the computational tasks and the storage of metadata