Daniel Krpelik

portrait I have been born, raised and educated in Czech Republic, EU. So far I have acquired Master’s degree in Applied Mathematics at VŠB-Technical University of Ostrava and am currently pursuing PhD degree at the same institution together with PhD studies at the Durham University.

The Department of Applied Mathematics at the university in Ostrava emphasizes greatly the numerical methods for engineering. I was therefore extensively trained in Finite Element and Boundary Element methods with accompanying algorithms for quadratic programming, non linear programming, and solving of linear systems.

Later, during my studies, I have focused on the theories of uncertainties, because I have found, that here lies the narrow bottleneck we have to master in order to assess our confidence in any simulation results. We always have to make assumptions while reasoning about the real world and statistics helps us to discriminate the incorrect ones (because of from incorrect assumptions one can deduce anything, including fallacies).

My research focuses on numerical methods quantifying and utilizing uncertainties. I have worked on the problems of statistical inference, mostly within the framework of Bayesian statistics, and consequent decision making under uncertainty. A little different, but with a lot of common themes, are the numerical methods which utilize random processes like Monte Carlo methods and bio-inspired optimization. These allow us to solve problems which would be intractable otherwise. The drawbacks are that we can never be entirely certain about the convergence of these methods, so deep and exact analysis is needed.

I have spent two years employed as a research assistant at IT4Innovations supercomputer centre at the university in Ostrava developing algorithms for medical image processing. Our research was carried out in collaboration with the nearby university hospital. There my interest in uncertainty theories, other than probability theory, have arisen. During the research I have started to search for possible ways to utilize expert knowledge (from the field of medical anatomy) for the task of Computed Tomography image segmentation. The probability theory approach contained several drawbacks. Mainly, we have lacked necessary amount of “labeled” data to make proper statistical inference. In other words, one has to solve the problem in order to solve the same problem (this is common to machine learning methods). I have decided to step aside for a while in order to research other approaches.

I will be working on the UTOPIAE ESR8 position under the supervision of Professor Coolen and Dr Aslett. My task is to develop methodology, based on improper probability, to estimate system reliability during different design phases. The reliability can be, of course, estimated once we construct (a lot of) working prototypes and carry on necessary experiments (break them), but such an approach would be very ineffective considering both time and expenses. My work should allow us to instead plan a series of cheaper experiments and aggregate these partial results in order to drive the overall design all the way from the beginning.

If successful, we might be yet another step closer to boldly go where no man has gone before.

Objectives: To develop suitable theory of system reliability quantification, using imprecise probabilities, in order to reflect carefully the uncertainties involved in this process at different stages; To derive an approximation of the lower and upper probabilities of system functionalities; To upscale to the propagation of upper and lower previsions to large systems; To study a representation of uncertainty in multi-phased design of aerospace systems.

Expected Results: A theoretical and computational framework for system reliability quantification in multi-phase processes using Imprecise Probability Theory. A theoretical and computational framework for robust optimisation and decision making in multi-phase processes. A demonstrative example of application to the life cycle assessment of a launcher. New methods for system reliability quantification at different stages of system design, reflecting indeterminacy in the specification of the required functionality and providing the opportunity to focus on robustness with regard to resilience of the system. New computational methods, including the use of approximations, to enable upscaling of recently present-ed theory of imprecise probabilities for system reliability to large real-world multi-phase processes.

Planned Secondments: SU (M27-29) to work on the application of imprecise probabilities and expert elicitation to the end-to-end design of space systems within WP3.3 and WP3.5, ESTECO (M37-39) to work on the application of the pro-posed methodology to multidisciplinary model-based collaborative system engineering within WP3.4 and 3.5.