Data-Driven Modeling of Nonlinear Delay Differential Equations with Gap Effects using SINDy

Jiamin Xu

Abstract:

An accurate modeling approach to predict the
trajectory of a drillstring plays a critical role in drilling
operation. Nonlinear Delay Differential Equations (DDEs) have
been considered as an effective tool to serve the purpose. This
paper introduces a novel data-driven approach to model the
borehole propagation dynamics by incorporating nonlinear
DDEs with Linear Complementarity Problem (LCP) using the
Sparse Identification of Nonlinear Dynamics (SINDy) method.
The developed model can predict borehole propagation without
relying on physics-based information while retaining the same
dynamics as those predicted by physics-based nonlinear DDEs.
To assess the resilience of the proposed approach, we introduce
noise into the dataset, demonstrating the robustness of the
SINDy method. Additionally, a stability analysis of the data-
driven DDEs offering insights into its reliability and potential
applications.