Modelling Ultrasonic Inspection of Branched Stress Corrosion Cracks using Machine Learning and AI


Stress corrosion cracking (SCC) may lead to sudden and catastrophic failure, if left undetected or incorrectly characterised. The temporary shutdown by EDF of five nuclear reactors in France in 2021 [1], after the detection of SCC, emphasises the severity of the threat posed by this phenomenon. One method to detect and to characterise SCC is ultrasonic non-destructive evaluation (NDE), which uses reflection and scattering of high frequency (typically in the range of MHz) sound waves to obtain an internal picture of a component or structure, without causing any damage. A key research question is how best to combine theoretical, semi-analytical (combination of theoretical and numerical methods), and numerical methods to model the scattering of ultrasound from highly complex, branched defect species, typical of SCC, to improve NDE inspection design and qualification. The models, optimised using insight gained from experimental analysis of real SCC defects, as done previously for thermal fatigue [2], will be used to generate an extensive synthetic database covering a range of defect and inspection parameters identified by our partners in the Research Centre for Non-Destructive Evaluation (RCNDE) as being industry-relevant priorities. The other key research question addressed in this project relates to the development and validation of machine learning and AI algorithms, which will be optimised using a continual feedback loop between this database, models, and algorithms. The project is important because of the long-standing and challenging requirement for the cost-effective measurement of SCC, as well as the industrial priority for adoption of artificial intelligence in inspection systems to allow for remote decision making and inspection.

The project will develop a combination of theoretical mathematical techniques, numerical methods, and Machine Learning algorithms to improve the modelling of the ultrasonic inspection of highly complex and challenging defect species that pose a critical safety risk for industrial plant. It will complement the RCNDE Core Project MUSICA (Modelling UltraSonic Inspection of Challenging defects for Automated analysis, starting March 2023), extending the work there for thermal fatigue and hydrogen cracking to branched stress corrosion cracks. The project will consider a wide range of ultrasonic inspection techniques, beyond conventional single crystal scanning, including phased array and full matrix capture. The successful candidate will work as part of an ultrasonic NDE group in the Department of Mathematical Sciences and the Signal Processing group in Electrical Engineering and Electronics at the University of Liverpool.

Person Specification

We are seeking a highly motivated candidate who should have a strong background in applied mathematics, as evidenced by a first-class (or strong upper second-class) MMATH/BSc in Mathematics, Engineering or Physics with a substantial applied mathematics focus (or equivalent). Applicants with a relevant MSc incorporating a substantial element of applied mathematics, acoustics/ultrasonics, structural mechanics, machine learning are also very much welcomed. Preferred skills include a strong mathematical background, a keen interest in machine learning and AI algorithms, programming, and excellent writing, communication, presentation, and organisation skills.

The project will be undertaken in collaboration with the main industrial partner EDF and the project’s industrial supervisor (Dr. John Jian, EDF). There will be multiple opportunities to interact with other industrial stakeholders via RCNDE events throughout the 4-year project. The successful applicant will receive formal training in the analysis of partial differential equations (including functional analysis, fundamental solutions, Green’s functions), and machine learning algorithms. However, prior experience in any of these areas would be advantageous.

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Please quote the title of the project (Modelling Ultrasonic Inspection of Branched Stress Corrosion Cracks using Machine Learning and AI) and the reference number MPPR003 when applying.



Open to students worldwide

Funding information

Funded studentship

The successful candidate is expected to start at the University of Liverpool in October 2023 (at the start of the academic year 2023/34).

The project is a 4-year fully funded EPSRC Industrial CASE studentship with the industrial partners being the Research Centre for Non-Destructive Evaluation (RCNDE) and EDF. The funding will cover UK tuition fees, maintenance above the average UKRI Doctoral Stipend rate (presently the minimum stipend rate is £17,668 per annum to be updated in Spring 2023), including a generous annual top up from RCNDE/EDF (subject to contract) and an allowance for training, secondment, conference, equipment, and research expenses.




[2] S.G. Haslinger et al. Insight, 63(1). (2021)