Online drill-system parameter estimation and hazardous event detection

Student thesis: Doctoral ThesisPhD


The use of on-line, noisy, partial observations as a means of inferring obscured system parameters is one that arises in a number of applications. Hydrocarbon drilling operations are one such example, in which the presence of hazardous events and general subsurface activity must often be inferred using measurements of the drill equipment taken at the surface. Adopting a Bayesian viewpoint, the task is then to estimate or --- where possible --- exactly compute the probability distribution of the parameters as the corresponding measurements are assimilated.
If the latent parameters are assumed to form a Markov process then the described statistical model has sufficient structure for the implementation of a number of inference methods. In applications where the underlying mappings are non-linear, the distributions are generally intractable and sequential Monte Carlo (SMC) methods offer a means of constructing estimates. For their relative robustness and versatility, SMC methods are often advantageous over other approaches. However, their construction requires repeated generation of weights based on the map between the parameter space and the observation space. If this weight generation cost is expensive then the repeated computation of these terms can limit the usefulness of the method in applications such as the drilling operation.
In this thesis we present a novel SMC method called the multilevel bootstrap particle filter (MLBPF) that arises from applying the approach of multilevel Monte Carlo (MLMC) to the weight computation step. The aim of this adaptation is to translate the efficiency savings of MLMC to the SMC setting, thus enabling more accurate estimates to be constructed with the same computational budget. Despite the relative simplicity of the idea, the implications it has on the method are profound, since in general the weights are no longer guaranteed to be non-negative. In addition to specifying an operational MLBPF algorithm, we prove a strong law of large numbers and central limit theorem result, before numerically testing the MLBPF on a number of models comparable to the drill-system. In addition to attaining empirical accuracy gains in these experiments, we derive a general approach to particle filtering on drill-system type models that provides a means of estimating the hidden parameter distributions in the absence of exact knowledge of the underlying system state.
Date of Award13 Oct 2023
Original languageEnglish
Awarding Institution
  • University of Bath
SupervisorKari Heine (Supervisor) & Mark Opmeer (Supervisor)


  • Sequential Monte Carlo methods
  • Multilevel methods
  • Mathematical modelling
  • Partial differential equations

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