EPSRC DTP PhD studentship: Hierarchical Multilevel Markov Chain Monte Carlo Algorithms for Accelerated Certification in Advanced Manufacturing

University of Exeter - College of Engineering, Mathematics and Physical Sciences

Supervisors:
Main supervisor: Dr Timothy J Dodwell (University of Exeter)
Co-supervisor:  Prof. Oana Ghita (University of Exeter)
Co-supervisor:  Prof. Peter Challenor (University of Exeter)

Project Description:
Additive manufacturing (AM) is a rapidly growing technology which fabricates complex geometric components by depositing material on a layer-by-layer approach. The basic advantages of additive manufacturing are well proven, yet it is often compromised by high costs, long development times and significant material and process-induced variability. For high value manufacturing industries (e.g. aerospace) where safety is paramount, risk is quantified by conservative safety factors derived from extensive physical testing. The introduction of novel materials or designs requires prohibitively expensive recalibration of tests. This bottleneck paralyzes the rapid design of new products and materials.

The student will develop novel Multilevel Markov Chain Monte Carlo (MLMCMC) methods, which will reduce the reliance on expensive physical testing to certify additively manufactured products. These stochastic algorithms powerfully combine relatively few experimental tests with CT images of defects and a hierarchy of mathematical models to provide efficient, robust and safe (reliable) estimates for distribution of a components strength given the presence of manufacturing variability. It is envisaged the PhD will study three areas 

  1. Developing a method to characterise the distribution random defects in manufactured parts from CT images for inputs into the mathematical models.
  2. Speed-up existing MLMCMC algorithms by generating a gradient-informed proposal distribution for the Markov Chains.
  3. Demonstrate the new methods for an industrial test case set by Airbus.

The PhD topic offers an exciting interdisciplinary mix between engineering, mathematics and high performance computing with strong industrial links. These skills would be highly desirable for career paths both in academia and industry. The background of the supervising team will provide specialist training in each of the areas of Engineering Mathematics (Dodwell), Statistics (Challenor) and Manufacturing (Ghita).

Existing collaborations with Heidelberg (Bastian) for high performance computing and MIT ( Marzouk) for industrial applied Bayesian Inverse problems will provide the PhD a unique opportunity to visit these leading research institutions and develop international links. In particularly this will include Heidelberg’s funded summer school courses in high performance computing.

Industry partners Airbus, have agreed a period of secondment to Filton, Britsol, giving invaluable industry experience. The hope is this will initiate the commercial impact of the academic results generated during the PhD.

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Type / Role:

PhD

Location(s):

South West England