The loading and resulting deformation resulting from explosive detonations has wide-reaching effects on different people ranging from civilian populations in conflict areas to instances where accidents result in damage. A significant amount of thought and resources is invested into protecting key infrastructure and people from damage in these situations. Typically, if we fully understand the pressure loading pulse both temporally and spatially, we are much better able to predict the resulting deformation of structures allowing us to much better design protection that would withstand this loading.

The challenge of understanding the loading ensuing detonation of highly energetic materials is a very complex one that is an ongoing funded area of research with new breakthroughs in understanding happening at Sheffield in existing EPSRC grants. This project seeks to address this gap in knowledge by developing a method to determine the characteristics of the blast pressure loading based on observed structural deformation and damage.

In this project transient deformation data will be extracted using the techniques of Ultra high speed imaging and Digital Image Correlation established by the supervisory team and this project will make use of a machine learning technique known as the Gaussian process latent force model approach, which has already seen some use at larger length-scales and across longer time-scales to determine loads. For example in determining loading from wind or waves on offshore platforms [1,2]. This methodology is a physics-informed machine learning approach which combines engineering expertise regarding the dynamics of a structure with the right source of information found in real-time sensing. The current proposal aims to push this technique further by studying events with severely nonlinear behaviour, with high degrees of spatial and temporal variations in loading, and complex strain-rate dependent response of materials. Furthermore, moving from the well-established point force method to one which incorporates distributed loading is non-trivial and will see the analysis move from sets of ordinary to partial stochastic differential equations.

These complications motivate research into developing the methods currently available beyond their present capability, and necessitate studying a number of simple baseline cases first. The project will begin with simplified models and loading scenarios to build confidence in the approach. First, using basic structural models with simple, well-defined loads, the goal is to test whether established inverse methods can successfully identify key blast parameters. As the project progresses, more complex models will be developed that simulate distributed loading over a structure.

This project aims to be in a position to handle the most challenging scenario: complex structural models combined with complex loading conditions. But to reach this stage a fundamental understanding of the limitations of the technique and where the assumptions breakdown is needed. As the project progresses more sophisticated physics, e.g. nonlinear dynamic behaviour and plastic deformation, will be included to improve accuracy and certainty about the load. Finally, it will be necessary to make modifications to the underlying machine learning methodologies, to move to non-stationary or deep Gaussian process models and/or to consider extensions to spatio-temporal Gaussian process state-space representations.

These complications motivate research into developing the methods currently available beyond their present capability, and necessitate studying a number of simple baseline cases first. The project will begin with simplified models and loading scenarios to build confidence in the approach. First, using basic structural models with simple, well-defined loads, the goal is to test whether established inverse methods can successfully identify key blast parameters. As the project progresses, more complex models will be developed that simulate distributed loading over a structure.

This project aims to be in a position to handle the most challenging scenario: complex structural models combined with complex loading conditions. But to reach this stage a fundamental understanding of the limitations of the technique and where the assumptions breakdown is needed. As the project progresses more sophisticated physics, e.g. nonlinear dynamic behaviour and plastic deformation, will be included to improve accuracy and certainty about the load. Finally, it will be necessary to make modifications to the underlying machine learning methodologies, to move to non-stationary or deep Gaussian process models and/or to consider extensions to spatio-temporal Gaussian process state-space representations.

In summary, this project draws on experience of leading research streams within the MAC school, utilising prior knowledge and understanding to substantially reduce the risk of the project, leading to significant advancements in each respective field, and, more importantly, leveraging their combination of expertise to contribute a new generation of tools.

Interested candidates are strongly encouraged to contact the project supervisors to discuss your interest in and suitability for the project prior to submitting your application.

Please refer to the EPSRC DLA webpage for detailed information about the EPSRC DLA and how to apply.