In high-value manufacturing sectors such as aerospace and nuclear, safety is paramount. For this reason, the design and qualification of inspection for safety-critical components is a crucial part of the overall development cycle. However, current practice makes extensive use of experimental trials on physical components and mock-ups, into which artificial defects, limited to small numbers of specific test cases, must be introduced to demonstrate that they can be detected and characterised. Inspection qualification is therefore extremely time-consuming and costly (with some full mock-ups of defect-containing components costing £millions), and at odds with the general move toward agile, small-batch, bespoke, digitally-enabled manufacturing. We propose replacing the use of these expensive, wasteful, physical test specimens with digital alternatives, to improve manufacturing efficiency. Delivering this will require high-speed, representative, realistic numerical simulation capabilities to be developed, in combination with solutions to reliably sample and interpolate across the high dimensionality of the parametric space. This virtual testing capability will enable the inspection of a high value component to be designed, optimised, and qualified before a single part has been manufactured. It will provide the basis of a simulation tool for operator training and be able to generate data at the scale and fidelity needed to train future machine learning solutions for inspection automation. Ultrasonic array inspection will be the demonstrator case as this is the most widely used method for assessing the internal integrity of safety-critical components, both at manufacture and in service. To achieve the goal requires validated tools to synthesise authentic inspection data at scale and a methodology to robustly explore the vast parameter space of possible defects to determine inspection performance. Our idea to achieve this ambitious vision is to approach the problem from two complimentary directions. Bottom-up: we will make the direct numerical simulation of raw data more efficient. Building on previous world-leading research by the applicants, we will show how numerical simulation tools can be better exploited to reduce the computational burden by at least one order of magnitude. Top-down: we will make the quantitative characterisation of the multi-dimensional parameter space to qualify inspection performance more efficient. Drawing on our domain knowledge and in extensive discussion with industrial collaborators (Rolls-Royce, EDF, Jacobs, Airbus, and KANDE), we will develop suitable surrogate modelling, sampling, and integration strategies for accurately characterising the parameter space with a small number of high-fidelity numerical simulations. In addressing this problem we will produce a set of tools and techniques that ensure that inspection qualification is reduced in cost and complexity by orders of magnitude, leaving it fit for the future of digital manufacturing.

In March 2011 a magnitude-9.0 earthquake struck in the Pacific Ocean off the northeast coast of Japan's Honshu island. Named the Great East Japan Earthquake by the Japanese government, it triggered a massive tsunami that flooded more than 200 square miles of coastal land. This devastating disaster caused a series of catastrophic failures resulting in the meltdown of the Fukushima Daiichi Nuclear Power Plant (NPP) and initiated a nuclear emergency. Reactor meltdown occurs when the cooling systems used to maintain and control the temperature of the nuclear fuel fails. The fuel then heats up uncontrollably and breaches the containment vessel or creates enough pressure to cause an explosion. Reactor meltdown occurred at all three reactors at Fukushima, resulting in fuel debris being dispersed throughout the reactors. Retrieval of the fuel debris from the Fukushima Daiichi NPP is of great importance for decommissioning and waste management. It requires detailed understanding of the radioisotope composition within the debris and knowledge of their location. However, inside the stricken reactors' containment vessels, the radiation levels are so intense it presents a significant challenge. It prevents direct human intervention, can overwhelm detectors and sensors, damage electronics and cause materials to perish. Access routes to inside the containment vessels are also very narrow. To make general observations, identify fuel debris composition, location and retrieval, dedicated robots are deployed. Many of the robots deployed to date have failed due to radiation damage during operation or their function is severely hampered by the extreme environment. This project brings together two world-leading research activities in the United Kingdom associated with radiation-hard, portable radiation detection (Lancaster University) and the development of small, radiation-hard remotely-operated vehicles (The University of Manchester) in collaboration with Okayama University and Kobe City College of Technology who have pioneered radiation-hard processors. The key aim of the research is to develop and deploy a simplified robot that prioritises radiation hardness and reliability over functional complexity. The hypothesis is, 'can such robots be more effective than the sophisticated alternatives tried to date?'. The ground-based radiation-hard robot will be equipped with non-destructive sensors for remote inspection. A radiation tolerant payload consisting of radiation sensors and LiDAR (light detection and ranging) will afford 3-dimensional (3D) spatial mapping of highly radioactive environments superimposed with located radiation intensities and radioisotope identities. The robot will be tested in realistic fields to demonstrate its ability to locate and identify dispersed radioisotopes derived from nuclear fuel debris inside Fukushima's stricken reactors. Such technology is also applicable to the UK's nuclear decommissioning challenges, specifically at Sellafield Site Ltd., and world-leading research in fusion energy at the UK Atomic Energy Authority.

CRADLE brings together the industrial experience that Jacobs have in applied Robotics and Autonomous Systems (RAS) with the research expertise at the University of Manchester in this field, to create a collaborative research centre that is internationally leading and sustainable in the long-term. Our vision for CRADLE is that it will deliver novel and transformational RAS technology for demanding environments, such as space, nuclear, energy generation and urban infrastructure, allowing the benefits promised by this technology to be realised across wide sectors of UK industry. Whilst there has been significant progress made in robotic systems in recent years, the step to truly autonomous robotics and smart machines, which will deliver the greatest impact to UK industry, remains a significant barrier, particularly in complex, demanding and heavily regulated environments. Here, incorrect decisions and inappropriate actions can have significant consequences, such as the release of radioactive materials or the loss of high value equipment. We have seen that incremental extensions to RAS components have not been sufficient to surmount this autonomy barrier and believe that a step change is required to: - create an autonomy-focussed framework that brings together the many independent robotic components that includes sensors, actuators, software and safety systems; - address key research gaps that exist in the specific components within this framework that affect the reliability, resilience and trustworthiness of the overall autonomous system; and - clarify, and embed, the wide range of end-user, business and regulatory constraints that must be accommodated within this framework for long-lasting autonomy. CRADLE has been guided by future industry needs and addresses major research obstacles to RAS development. Furthermore, CRADLE will create a pathway to impact that enables low-TRL RAS technologies to be developed and then translated into safe, reliable and innovative solutions that can be deployed to address long-term industry and societal problems in a range of demanding environments. We will focus on generic technologies that will allow RAS to be deployed across multiple industry sectors, and we will target specific use cases that will enable this technology to be demonstrated in sectors of particular importance to the industrial supply chain. These use cases will be drawn from sectors where Jacobs have existing capability, such as nuclear, space and urban infrastructure, but we will also explore areas of growing interest and opportunity, such as clean energy generation, sustainable transportation, healthcare and security.

Digital twins are a fusion of digital technologies considered by many leading advocates to be revolutionary in nature. Digital twins offer exciting new possibilities across a wide range of sectors from health, environment, transport, manufacturing, defence, and infrastructure. By connecting the virtual and physical worlds (e.g. cyber-physcial), digital twins are able to better support decisions, extend operational lives, and introduce multiple other efficiencies and benefits. As a result, digital twins have been identified by government, professional bodies and industry, as a key technology to help address many of the societal challenges we face. To date, digital twin (DT) innovation has been strongly driven by industry practitioners and commercial innovators. As would be expected with any early-adoption approach, projects have been bespoke & often isolated, and so there is a need for research to increase access, lower entry costs and develop interconnectivity. Furthermore, there are several major gaps in underpinning academic research relating to DT. The academic push has been significantly lagging behind the industry pull. As a result, there is an urgent need for a network that will fill gaps in the underpinning research for topics such as; uncertainty, interoperability, scaling, governance & societal effects. In terms of existing networking activities, there are several industry-led user groups and domain-specific consortia. However, there has never been a dedicated academic-led DT network that brings together academic research teams across the entire remit of UKRI with user-led groups. DTNet+ will address this gap with a consortium which has both sufficient breadth and depth to deliver transformative change.

We live in the "Era of Mathematics" (UKRI, 2018), in which mathematics research has deep and widespread impact. Medical imaging is enhanced using the theory of inverse problems. Predicting sewage contamination in waterways after storms requires solving complicated systems of hydrodynamic equations. Machine learning tools are revolutionising data-intensive computing and, handled with proper mathematical care, have vast potential benefits for science and society. These are examples of the ongoing explosion in mathematical innovation driving, and being driven by, the analysis and modelling of data running through every aspect of life. Cutting-edge research now sits at the interface of data science and mathematical modelling. Methods and fields such as compressed sensing, stochastic optimisation, neural networks, Bayesian hierarchical models - to name but a few - have become interwoven and contributed to the delivery of a new domain of research. We refer to this research interface as "statistical applied mathematics". Established in 2014, the Centre for Doctoral Training in Statistical Applied Mathematics at Bath (SAMBa, samba.ac.uk) delivers leading research and training in this space. In the development of this bid, we have consulted widely with academic, industrial, and governmental partners, who consistently report a large and widening gap between demand and supply for highly skilled graduates. Our vision is to create a new generation of statistical applied mathematicians ready to lead high-impact, data-driven, mathematically-robust research in academia and industry. We will nurture a vibrant culture of cohort learning, enabling internationally-leading training in modern mathematical data science. A particularly important research focus will be the synthesis of data-driven methods with robust mathematical modelling frameworks. Tomorrow's industrial mathematicians and statisticians must understand when machine learning tools are (and are not) appropriate to use and be able to conduct the underpinning research to improve these tools by integrating scientific domain knowledge. This research challenge is informed by deep partnerships with a range of industry and government bodies. Our long-term partners such as BT, Syngenta, Novartis, the NHS, and the Environment Agency co-create our vision and our training. They are emphatic that we must address the urgent need for mathematical data science talent in this key strategic area for the UK economy. Many of our students will work directly on industry challenges during their PhD either in their core research or with internships. Our unique Integrative Think Tanks are the key mechanism for exploring new research ideas with industry. These are week-long events where SAMBa students, leading academics, and partners work together on industrial and societal problems. SAMBa graduates will be able to develop and apply new ideas and methods to harness the power of data to tackle challenges affecting society, the economy, and the environment. Our students will move into academia, providing sustainability to the UK's capacity in this field, as well as industry and government, providing impact through societal benefits and driving economic growth. Many alumni now hold permanent positions at leading UK universities and senior positions in a range of businesses. The CDT will be embedded within the University of Bath's Department of Mathematical Sciences, where 98% of the research is world leading or internationally excellent (REF2021). The CDT is supported by 58 academics in maths, with similar numbers of co-supervisors from industry and other departments. The centre will be co-delivered with 22 industry and government partners. A vital international perspective is provided by a worldwide network of 11 academic institutions sharing our scientific vision.