This page provides a catalogue of current and completed projects delivered through the Industrial Mathematics Internships programme.
The partners in this Internship were Barnett Waddingham and the University of Southampton. It is part of the KTN's Industrial Mathematics Internships Programme, co-funded by EPSRC.
The internship developed modern Bayesian statistical methodology to model insurance claims data. This type of modelling has been increasingly widely adopted in Health Sciences, but is relatively undeveloped in the insurance industry, where it is arguably equally relevant. It has the potential to add significant value to existing and future data resources.
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The partners in this Internship were VR Technology, the University College London and the University of Birmingham. It is part of the KTN's Industrial Mathematics Internships Programme, co-funded by EPSRC.
The project enabled VR Technology to improve upon their existing VGM algorithm incorporating aspects of Bühlmann models with microbubble theories, essentially extending the range of depths over which their model can be used whilst maintaining substantial customisability for both the company and the user.
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The partners in this Internship were Paradigm Geophysical and the University of Oxford. It is part of the KTN's Industrial Mathematics Internships Programme, co-funded by EPSRC.
The internship is in the area of inverse problems and occurs within the discipline of oil reservoir engineering. The objective was to modify an existing deconvolution algorithm used in the analysis of pressure transient data to smooth out the derivative response so that it appears more like a physical response (i.e. continuous). The project involved a regularised optimisation approach based on existing theory.
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Modelling of complex corroding industrial systems is critical to effective inspection and maintenance for assurance of system integrity. We model wall thickness and corrosion rate for multiple dependent corroding components, given observations of minimum wall thickness per component. At each inspection, we do not require that the whole system is observed. We adopt a Bayes Linear approach simplifying parameter estimation and avoiding often-unrealistic distributional assumptions. We also estimate key model variances, making exchangeability assumptions to facilitate analysis for sparse inspection time-series. The model is applied to inspection data from pipework networks on a full-scale offshore platform.
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As the use of microbiomics data becomes more mainstream, the analysis of the associated error must become more reliable. The type of data produced are very different from those generated by traditional microbiological sampling, notably by their richness of information. However, the interpretation is not as straightforward, and requires the use of advanced bioinformatics techniques. In order to test a hypothesis, the results must also be reliably related to a model, and this is best done if the model if quantifiable, for example using Systems Biology.
Microbiomics therefore presents many challenges to industrial mathematics, specifically in relation to raw data interpretation, error analysis and hypothesis testing. All three areas present distinct mathematical challenges in themselves and in order for microbiomics to be truly useful to a specific problem, these challenges must be tackled simultaneously.
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The partners in this Internship are Procter & Gamble and the University of Strathclyde.
Detergent-spray drying towers bring atomised slurries into contact with hot air to form powdered laundry detergent particles. As well as drying in the tower, the droplets also collide and agglomerate as they are transported through the tower. The particle size and shape of the product are dependent on these phenomena. The extent of agglomeration can also limit the capacity of the towers. P&G would like to model the collision and agglomeration phenomena and predict the particle sizes that are produced.
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The partners in this Internship are Airbus and Nottingham University. This project is funded by the Engineering and Physical Scienes Research Council.
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The partners in this Internship were Lein Applied Diagnostics and the University of Southampton.
Lein Applied Diagnostics has developed an innovative technology to optically measure a number of parameters of the body via the eye. One of Lein’s main areas of interest is the non-invasive measurement of glucose for people with diabetes. The aim of the project was to support the processing of clinical data from the RBH trial and from in-house tests to improve the correlation model between the eye and blood.
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The partners in this Internship are Airbus and Sheffield University. This project is funded by the Engineering and Physical Scienes Research Council.
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The partners in this Internship are NAG and Nottingham University. This project is funded by the Engineering and Physical Scienes Research Council.
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The partners in this Internship were Willis and the University of Oxford. This project is funded by Natural Environment Research Council.
Willis is currently investing significant resources in the development of the next generation of catastrophe models for support of the transactional business. The intern looked at speeding up an existing tool for optimising the placement strategy of client reinsurance programmes using Nereus.
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The partners in this Internship are Willis and King's College London. This project is funded by Natural Environment Research Council.
Willis is currently investing significant resources in the development of the next generation of catastrophe models for support of the transactional business. The intern will be looking at speeding up an existing tool for optimising the placement strategy of client reinsurance programmes using GPGPU.
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This project focused on three areas: Understanding the theoretical complexity of scheduling in OpenCL accelerators; designing scheduling algorithms for OpenCL accelerators; designing algorithms for MIMO signal decoding.
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This Internship project was carried out at Arup, in conjunction with the University of Warwick. The project focused on the development of novel mathematical approaches to the problem of dynamic image based lighting.
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This Internship project is being carried out at Roxar, in conjunction with Bournemouth University. The project focuses on the use of Graphical Processing Units (GPUs) in oilfield reservoir simulation.
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The partners in this Internship were BT and the University of Birmingham.
Network optimisation under uncertainty, that is combinatorial optimisation problems with stochastic data input. The aim was to construct a mathematical model that would enable to find optimal solutions in cases when deterministic problems are perturbed by unforeseeable changes of data, such as delays due to faults, severe weather conditions or breakdowns.
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This Internship project was carried out at the Met Office, in conjunction with the London School of Economics. The project focused on the application of Bayesian networks to evaluate climate risk and examines the usefulness of such approaches to informing and influencing real-world decision making processes.
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The partners in this Internship were Airbus and The University of Edinburgh.
The project involved defining a mathematical language to allow the capture of specification constraints, functional properties and test objectives on Airbus systems within appropriate logic formalisms and expressing modelled functions in adequate co-related algebras. The application of process calculus will help the verification and validation of complex mechatronic systems in Airbus. A simplified braking system was used as a case study.
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The partners in this Internship were National Grid (NG) and the University of Edinburgh.
The aim of the project was to calculate the probability of loss of supply given the actual incidence of faults on the GB transmission system. This involved looking in detail at plant types on the system, their associated failure rates, system load levels, the consequence of system faults and the interaction with the wholesale electricity market to determine the actual level of security of supply the system is providing to key loads.
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The partners in this Internship are Dstl and Cambridge University. This project is funded by the Engineering and Physical Scienes Research Council.
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The partners in this Internship were National Grid and University College London.
The project focused on the application of mathematical and statistical methods to identification of correlations of wind fleet outputs.
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The partners in this Internship were Airbus and Glasgow Caledonian University.
The project involved mathematical modelling of the designated braking system to compare flight data with simulation results. A dynamic model was developed based on the analysis of friction/slip characteristics identified from flight test data. A range of data fitting techniques were explored. Validation of the model was carried out and the trade-offs between accuracy, complexity and computational performance were investigated.
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The partners in this Internship were Bioinnovel Limited and University of Strathclyde. Bioprocessing, for example the production of stem cells, is a growing industrial area in the UK and at present the industry approach is to use invasive, in-line sampling of the mixture and statistical process control techniques. This project will make use of fundamental modelling, allied with noninvasive sampling, which will be a major shift in the field and will help promote the role of the industrial mathematician.
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The partners in this Internship were British Swimming and Sheffield Hallam University. This was the first time that British Swimming has considered modelling for optimising diving performance. This project was important in disseminating the usefulness of using mathematical modelling to understand complex interactions (such as that between athletes and equipment.)
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Under the forthcoming Solvency II risk management framework for the insurance industry, the preferred method for estimating risks is the 1-year value-at-risk (VaR) method, instead of the run-off method. The 1-year VaR method also assesses the risk-based capital, but with the difference that it only considers the variability within the next year. The aim of this internship project was therefore to extend Barrie & Hibbert’s current mortality model by incorporating a stochastic trend factor, in a way that will enable it to capture a significant risk factor under the new framework.
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The focus of the Internship project was assessing the relative benefits of the two internal ballistics software packages, namely FNGUN1D and FNGUN2D, and to understand mathematically when to make decisions based on a 1D simulation alone, whether the results are reliable and whether significant differences occur in the 2D simulations. As part of the internship a conference paper was generated.
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The partners in this Internship are Numerical Algorithms Group Ltd (NAG) and the University of Birmingham. The principal goal of this project will be to adapt NAG’s global optimisers to run on multi-processor machines, using either (or both) shared memory and message-passing paradigms, to speed –up the solution of large problems. It is anticipated that this will require changes to the algorithms themselves, and result in new software that will eventually be included in NAG products.
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The focus of the Internship project was to develop models that would help determine the mix of business in insurance portfolios to provide the highest return or minimum risk. The tools developed during the project will be used to advise Lloyd’s of London and its Syndicates on how to manage the balance between risk and return.
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In the property and casualty insurance industry, the underwriting cycle is characterized by alternating periods of rising and falling price adequacy. In simplest terms, this cycle is a product of supply and demand (where supply is equivalent to industry surplus). However, supply is driven by numerous factors; prior profitability, natural catastrophes, interest rates, investment returns, the availability of new capital, social and economic trends, and a host of other considerations can meaningfully affect the cycle. Further, price adequacy can vary substantially by region, industry, or product type.
The focus of the project was to develop a comprehensive simulation model of this system of pricing cycles.
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The Internship project primarily involved modelling and analysis of large disaggregated panel data sets of supermarket transactions. It fit into the overall aim of developing a holistic model of shopper behaviour, taking into account heterogeneity in their demographic profile, as well as past responses to pricing, promotion and marketing strategies.
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This project forms part of the LSC Group R&D project called "Deployable Decision Support Environment" (DDSE). DDSE is an integrated modelling environment for the prediction of through life support characteristics of capital assets. The environment includes both analytical and simulation based predictive capability and will accommodate consideration of both through life affordability and performance.
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