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A generalized additive model (GAM) explores the extent to which a single output variable of a complex system in a noisy environment can be described by a sum of smooth functions of several input variables.
Bath research has substantially improved the estimation and formulation of GAMs and hence
This improved statistical infrastructure has resulted in improved data analysis by practitioners in fields such as natural resource management, energy load prediction, environmental impact assessment, climate policy, epidemiology, finance and economics. In REF impact terms, such changes in practice by practitioners leads ultimately to direct economic and societal benefits, health benefits and policy changes. Below, these impacts are illustrated via two specific examples: (1) use of the methods by the energy company EDF for electricity load forecasting and (2) their use in environmental management. The statistical methods are implemented in R via the software package mgcv, largely written at Bath. As a `recommended' R package mgcv has also contributed to the global growth of R, which currently has an estimated 1.2M business users worldwide [A].
Research by Gondzio (Maxwell Institute) on algorithms for large-scale optimization has led to major advances in the design of interior point methods (IPMs). The advances include new ways of exploiting centrality (1996-2008) as well as special preconditioning (2004) and warmstarting (2003, 2008) techniques. These techniques make it possible to solve more difficult optimization problems more quickly. Some of these have been implemented by all major commercial providers of optimization software including IBM, Gurobi, Mosek and FICO. The techniques have therefore had an economic impact on these companies and on thousands of their customers worldwide who now benefit from faster, more reliable methods to solve their challenging optimization tasks.
This case study demonstrates the benefits achieved when the mathematical and computational aspects of a computational fluid dynamics (CFD) problem were brought together to work on real-world aerodynamic applications. While earlier insight on the solution reconstruction problem was purely based on empirical intuition, research in the School of Mathematics at the University of Birmingham by Dr Natalia Petrovskaya has resulted in the development of the necessary synthetic judgement in which the importance of accurate reconstruction on unstructured grids has been fully recognised by the CFD researchers at the Boeing Company. Boeing has confirmed that the research has led to substantial resultant improvements in their products as well as gains in engineering productivity. For instance, wing body fairing and winglets optimization for the Boeing 787 has been done by means of CFD only. Implementation of CFD in the design of their new aircraft allowed Boeing to reduce the testing time in the wind tunnel for the 787 aircraft by 30% in comparison with testing carried out for Boeing 777. Efficient use of CFD in the design of new aircrafts has helped the Boeing Company to further strengthen their core operations, improve their execution and competitiveness and leverage their international advantage.
Spatial decomposition methods have been extended to apply to spatial, scale, and temporal domains as a result of work at the Numerical and Applied Mathematics Research Unit (NAMU) at the University of Greenwich. This work has led to a numerical framework for tackling many nonlinear problems which have been key bottlenecks in software design and scientific computing. The work has benefitted the welding industry in the UK because these concepts are now embedded, with parallel computing, in the industry's modern welding design process software.
Data assimilation is playing an ever increasing role in weather forecasting. Implementing four- dimensional variational data assimilation (4DVAR) is part of the long term strategy of the UK Met Office.
In this case study, an idealised 4DVAR scheme, developed by a team from the Universities of Surrey and Reading working with the UK Met Office, based on the integration of Hamiltonian dynamics and nonlinearity into data assimilation, has now been taken up by the Met Office. It is being used to evaluate options for improving operational 4DVAR. The simplicity of the scheme developed by this team has facilitated careful analyses of some generic problems with the operational model. The outcome includes direct impact on the environment and indirect impact on the economy, both through improvements in weather forecasting.
Research by Professor John Thuburn and his group at the University of Exeter has made several key contributions to the formulation and development of ENDGame, the new dynamical core of the Met Office weather and climate prediction model. ENDGame has been shown to deliver improved accuracy and better computational performance at high processor counts compared to the current operational dynamical core, directly impacting the technological tools available to the Met Office. These improvements will benefit users when ENDGame becomes operational in early 2014: the economic value to the UK of the weather forecasts produced by the Met Office has been estimated to be in excess of £600M pa, while climate change projections inform policy decisions on mitigation and adaptation with huge economic implications.
From 1995 Professor Munjiza's research at QMUL has led to the development of a series of algorithms which can predict the movement and relationship between objects. These algorithms have been commercialised by a range of international engineering and software companies including Orica, the world's leading blasting systems provider (via their MBM software package), and the software modelling company, Dassault Systems (via their Abaqus software). Through these commercialisation routes Munjiza's work has generated significant economic impact which is global in nature. For example, his predictive algorithms have enabled safer, more productive blast mining for Orica's clients — in one mine alone, software based on Munjiza's modelling approach has meant a 10% increase in productivity, a 7% reduction in costs and an annual saving of $2.8 million. It has also been used in Dassault Systems' Abaqus modelling software, which is the world's leading generic simulation software used to solve a wide variety of industrial problems across the defence, automobile, construction, aerospace and chemicals sectors with associated economic impact.
Ocean circulation accounts for much of the energy that drives weather and climate systems; errors in the representation of the ocean circulation in computational models affect the validity of forecasts of the dynamics of the ocean and atmosphere on daily, seasonal and decadal time scales. Research undertaken by the University of Reading investigated systematic model errors that resulted from data assimilation schemes embedded in the key processes used to predict ocean circulation. The researchers developed a new bias correction technique for use in ocean data assimilation that alleviates these errors. This has led to significant improvements in the accuracy of the forecasts of ocean dynamics. The technique has been implemented by the Met Office and by the European Centre for Medium Range Weather Forecasting (ECMWF) in their forecasting systems, resulting in major improvements to the prediction of the weather and climate from oceanic and atmospheric models. The assimilation technique is also leading to better use of expensively acquired satellite and in-situ data and improving ocean and atmosphere forecasts used by shipping and civil aviation, energy providers, insurance companies, the agriculture and fishing communities, food suppliers and the general public. The impact of the correction procedure is also important for anticipating and mitigating hazardous weather conditions and the effects of long-term climate change.
A computational aerodynamics design system (FLITE) developed by Swansea researchers has been of significant economic benefit to the aerospace industry. When introduced, the unstructured mesh FLITE approach was considered by BAE Systems to be a step change in their design cycle. Using FLITE, highly complex modern aerospace configurations could be analysed in short timescales. The FLITE system has since been utilised by a number of international organisations. Its use in the design of the BLOODHOUND project has also contributed to significant public engagement in science and engineering, including a large-scale education programme with which over 5,000 schools have fully engaged.
Research from the Sheffield Department of Mechanical Engineering has led to major improvements in engineering analysis and design software for aerospace companies such as Rolls-Royce and Airbus. As a result of introducing new practices based on our research, the organisations have reported significantly reduced time input to design components as well as related economic benefits. For example: Rolls-Royce has reported an order of magnitude improvement in the time needed to mesh components. Similarly, by adopting our highly efficient computational aerodynamics solvers, Defence Science & Technology Laboratory has reduced the time its engineers spent evaluating concepts from many days to a few hours.